Category: Probability

tHE TABLE BELOW SHOWS THE NUMBER OF STUDENTS IN EACH CLASS IN A SCHOOL. tHE PERCENTAGE (%) OF THE STUDENTS IN EACH CLASS WHO WEAR GLASSES IN ALSO SHOWN.

5/6/2023

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THE TABLE BELOW SHOWS THE NUMBER OF STUDENTS IN EACH CLASS IN A SCHOOL. THE PERCENTAGE (%) OF THE STUDENTS IN EACH CLASS WHO WEAR GLASSES IN ALSO SHOWN.

KCSE 2020 MATHEMATICS ALT A PAPER 2 QUESTION 24

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A bag contains 5 red, 4 white and 3 blue beads. Three beads are selected at random without replacement. Find the probability that

13/5/2023

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A bag contains 5 red, 4 white and 3 blue beads. Three beads are selected at random without replacement. Find the probability that

a) The first red bead is the third bead picked. (2mks)
b) The beads selected were, white and blue: (2mks)
i) In that order
ii) In any order (2mks)
c) No red bead is picked (2mks)
d) Beads picked are of the same colour. (2mks)

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Bag X contains 2 green marbles and 8 yellow marbles. Bag Y contains 4 green marbles and 5 yellow marbles. A bag is selected at random and two marbles drawn one at a time without replacement.

29/4/2023

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Bag X contains 2 green marbles and 8 yellow marbles. Bag Y contains 4 green marbles and 5
yellow marbles. A bag is selected at random and two marbles drawn one at a time without
replacement.

(a) Represent this information on a tree diagram (4 marks)
(b) Find the probability that:
(i) they are both green. (2mks)
(ii) they are both yellow and from bag X. (2mks)
(iii) the second ball is yellow. (2mks)

ANSWER

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THE PROBABILITIES THAT MUENI, AUMA AND WANJIKU ARE TIME BARRED TO VOTE FOR THEIR FAVORITE PRESIDENTIAL CANDIDATES ARE 1/4, 1/3 AND 3/4 RESPECTIVELY. ON THE DAY OF VOTING, WHat is the probability that;

10/4/2023

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THE PROBABILITIES THAT MUENI, AUMA AND WANJIKU ARE TIME BARRED TO VOTE FOR THEIR FAVORITE PRESIDENTIAL CANDIDATES ARE 1/4, 1/3 AND 3/4 RESPECTIVELY. ON THE DAY OF VOTING, WHAT IS THE PROBABILITY THAT;

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Auma, Hassan and Kamau competed in a game of darts. Their probabilities of hitting the target are 2/5, 1/5 and 3/10 respectively.

2/12/2021

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Auma, Hassan and Kamau competed in a game of darts. Their probabilities of hitting the target are 2/5, 1/5 and 3/10 respectively.

(a) Draw a probability tree diagram to show all the possible outcomes. (2mks)

(b) Calculate the probability that
(i) No one hit the target. (2mks)

(ii) Only one of them hit the target. (2mks)

(iii) At least one of them hit the target. (2mks)

(iv) At least one of them missed the target. (2mks)

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K.C.S.E Mathematics Q & A - MODEL 2019PP2QN06

24/9/2020

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Form 3 Mathematics

A bag contains 6 red counters and 4 blue counters. Two counters are picked from the bag at random, without replacement.
(a) Represent the events using a tree diagram.
(b) Find the probability that the two counters picked are of the same colour.

answers

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K.C.S.E Mathematics Q & A - MODEL 2018PP2QN14

21/9/2020

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Form 3 Mathematics

In a certain firm there are 6 men and 4 women employees. Two employees are chosen at random to attend a seminar. Determine the probability that a man and a woman are chosen.

answer

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K.C.S.E Mathematics Q & A - MODEL 2017PP2QN14

17/9/2020

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Form 3 Mathematics

A committee of 3 people was chosen at random from a group of 5 men and 6 women. Find the probability that the committee consisted of more men than women.

answer

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K.C.S.E Mathematics Q & A - MODEL 2005.PP1.QN.8

17/9/2020

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Form 3 Mathematics

Two teachers are chosen randomly from a staff consisting 3 women and 2 men to attend a HIV/AIDs seminar. Calculate the probability that the two teachers chosen are:

(a) Of the same sex
(b) Of opposite sex

Answer

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K.C.S.E Mathematics Q & A - MODEL 2016PP2QN09

15/9/2020

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Form 3 Mathematics

A bag contains 2 white balls and 3 black balls. A second bag contains 3 white balls and 2 black balls. The balls are identical except for the colours. Two balls are drawn
at-random, one after the other from the first bag and placed in the second bag. Calculate the probability that the 2 balls are both white.

answer

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K.C.S.E Mathematics Q & A - MODEL 2015PP2QN11

10/9/2020

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Form 4 Mathematics

In a nomination for a committee, two people were to be selected at random from a group of 3 men and 5 women. Find the probability that a man and a woman were selected

answers

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K.C.S.E Mathematics Q & A - MODEL 2004.PP1.QN.7

10/9/2020

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Form 3 Mathematics

In the year 2003, the population of a certain district was 1.8 million. Thirty per cent of the population was in the age group 15 – 40 years. In the same year, 120,000 people in the district visited the Voluntary Counseling and Testing (VCT) centre for an HIV test.
If a person was selected at random from the district in this year. Find the probability that the person visited a VCT centre and was in the age group 15 – 60 years.

Answer

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K.C.S.E Mathematics Q & A - MODEL 2014PP2QN21

8/9/2020

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Form 3 Mathematics

Each morning Gataro does one of the following exercises: Cycling, jogging or weightlifting. He chooses the exercise to do by rolling a fair die. The faces of the die are numbered 1, 1,2, 3, 4 and 5.
If the score is 2, 3 or 5, he goes for cycling. If the score is 1, he goes for jogging.
If the score is 4, he goes for weightlifting.
(a) Find the probability that:
(i) on a given morning, he goes for cycling or weightlifting;
ii) on two consecutive mornings he goes for jogging
(b) In the afternoon, Gataro plays either football or hockey but never both games. The probability that Gataro plays hockey in the afternoon is:
1/3 if he cycled;
2/5 if he jogged and
1/2 if he did weightlifting in the morning.
Complete the tree diagram below by writing the appropriate probability on each branch.

answers

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K.C.S.E Mathematics Q & A - MODEL 2013PP2QN09

3/9/2020

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Form 3 Mathematics

Two machines, M and N produce 60% and 40% respectively of the total number of items manufactured in a factory. It is observed that 5% of the items produces
by machine M are defective while 3% of the items produced by machine N are defective.
If an item is selected at random from the factory, find the probability that it is defective

answer

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K.C.S.E Mathematics Q & A - MODEL 2012PP2QN23

2/9/2020

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Form 3 Mathematics

A box contains 3 brown, 9 pink and 15 white clothes pegs. The pegs are identical except for the colour.
(a) Find the probability of picking:
(i) a brown peg;
(ii) a pink or a white peg.
(b) Two pegs are picked at random, one at a time, without replacement. Find the probability that:
(i) a white peg and a brown peg are picked;
(ii) both pegs are of the same colour.

answers

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K.C.S.E Mathematics Q & A - MODEL 2003PP1QN009

2/9/2020

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Form 3 Mathematics

There are three cars A,B and C in a race. A is twice as likely to win as B while B is twice as likely to win as c. Find the probability that.

a) A wins the race
b) Either B or C win the race. (3mks)

aNSWER

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K.C.S.E Mathematics Q & A - MODEL 2011PP2QN06

27/8/2020

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Form 3 Mathematics

The ages in years of five boys are 7, 8, 9, 10 and 11 while those of five girls are 4, 5, 6, 7 and 8. A boy and a girl are picked at random and the sum of their ages is recorded.
(a) Draw a probability space to show all the possible outcomes.
(b) Find the probability that the sum of their ages is at least 17 years.

answers

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K.C.S.E Mathematics Q & A - MODEL 2010PP2QN09

25/8/2020

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Form 3 Mathematics

A bag contains 2 white balls and 3 black balls. A second bag contains 3 white balls and 2 black balls. The balls are identical except for the colours, b
Two balls are drawn at random, one after the other from the first bag and placed in the second bag.
Calculate the probability that the 2 balls are both white.

answer

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K.C.S.E Mathematics Q & A - MODEL 2009PP2QN12

21/8/2020

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Form 3 Mathematics

On a certain day, the probability that it rains is 1/7 . When it rains the probability that Omondi carries an umbrella is 2/3. When it does not rain the probability that Omondi carries an umbrella is 1/6. Find the Probability that Omondi carried an umbrella that day.

answer

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K.C.S.E Mathematics Q & A - MODEL 2002PP1QN019

20/8/2020

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Form 3 Mathematics

During a certain motor rally it is predicted that the weather will be either dry (D) or wet (W). The probability that the weather will be dry is estimated to be ⁷_/10. The probability for a driver to complete (C) the rally during the dry weather is estimated to be ⁵/_6. The probability for a driver to complete the rally during wet weather is estimated to be ¹_/10.

Complete the probability tree diagram given below.

What is the probability that:-

i) The driver completes
ii) The weather was wet and the driver did not complete the rally?

Answer

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K.C.S.E Mathematics Q & A - MODEL 2008PP2QN06

17/8/2020

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Form 3 Mathematics

A student at a certain college has a 60% chance of passing an examination at the first attempt. Each time a student fails and repeats the examination his chances of passing are increased by 15%
Calculate the probability that a student in the college passes an examination at the second or at the third attempt.

answer

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K.C.S.E Mathematics Q & A - MODEL 2007PP2QN24

13/8/2020

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Form 3 Mathematics

Two bags A and B contain identical balls except for the colours. Bag A contains 4 red balls and 2 yellow balls. Bag B contains 2 red balls and 3 yellow balls.
(a) If a ball is drawn at random from each bag, find the probability that both balls are of the same colour.
(b) If two balls are drawn at random from each bag, one at a time without replacement, find the probability that:
(i) The two balls drawn from bag A or bag B are red
(ii) All the four balls drawn are red

answers

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K.C.S.E Mathematics Q & A - MODEL 2006PP2QN20

11/8/2020

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Form 3 Mathematics

(a) Two integers x and y are selected at random from the integers 1 to 8. If the
same integer may be selected twice, find the probability that
(i) x – y = 2
(ii) x – y is more
(iii) x>y
(b) A die is biased so that when tossed, the probability of a number r showing up, is given by p ® = Kr where K is a constant and r = 1, 2,3,4,5 and 6 (the number on the faces of the die
(i) Find the value of K
(ii) if the die is tossed twice, calculate the probability that the total score is 11

answers

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K.C.S.E Mathematics Q & A - MODEL 2001PP1QN23

21/7/2020

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Form 3 Mathematics

The probability of three darts players Akinyi, Kamau, and Juma hitting the bull's eye are 0.2, 0.3 and 1.5 respectively.

(a) Draw a probability tree diagram to show the possible outcomes
(b) Find the probability that:
- (i) All hit the bull's eye
- (ii) Only one of them hit the bull's eye
- (iii) at most one missed the bull’s eye

Answer

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K.C.S.E Mathematics Q & A - MODEL 2001PP1QN09

21/7/2020

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Form 3 Mathematics

A poultry farmer vaccinated 540 of his 720 chickens against a disease. Two months later, 5% of the vaccinated and 80% of the un-vaccinated chicken, contracted the disease. Calculate the probability that a chicken chosen random contacted the disease.

Answer

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KCSE MATHEMATICS QUESTIONS AND SOLUTIONS

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THE TABLE BELOW SHOWS THE NUMBER OF STUDENTS IN EACH CLASS IN A SCHOOL. THE PERCENTAGE (%) OF THE STUDENTS IN EACH CLASS WHO WEAR GLASSES IN ALSO SHOWN.

​​​​​KCSE 2020 MATHEMATICS ALT A PAPER 2 QUESTION 24

​ANSWER

​THE PROBABILITIES THAT MUENI, AUMA AND WANJIKU ARE TIME BARRED TO VOTE FOR THEIR FAVORITE PRESIDENTIAL CANDIDATES ARE 1/4, 1/3 AND 3/4 RESPECTIVELY. ON THE DAY OF VOTING, WHAT IS THE PROBABILITY THAT;

​Auma, Hassan and Kamau competed in a game of darts. Their probabilities of hitting the target are 2/5, 1/5 and 3/10 respectively.

(a) Draw a probability tree diagram to show all the possible outcomes. (2mks)

​(b) Calculate the probability that (i) No one hit the target. (2mks)

​(ii) Only one of them hit the target. (2mks)

​(iii) At least one of them hit the target. (2mks)

​(iv) At least one of them missed the target. (2mks)

Form 3 Mathematics

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11

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21

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9

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KCSE 2020 MATHEMATICS ALT A PAPER 2 QUESTION 24

ANSWER

THE PROBABILITIES THAT MUENI, AUMA AND WANJIKU ARE TIME BARRED TO VOTE FOR THEIR FAVORITE PRESIDENTIAL CANDIDATES ARE 1/4, 1/3 AND 3/4 RESPECTIVELY. ON THE DAY OF VOTING, WHAT IS THE PROBABILITY THAT;

Auma, Hassan and Kamau competed in a game of darts. Their probabilities of hitting the target are 2/5, 1/5 and 3/10 respectively.

(b) Calculate the probability that
(i) No one hit the target. (2mks)

(ii) Only one of them hit the target. (2mks)

(iii) At least one of them hit the target. (2mks)

(iv) At least one of them missed the target. (2mks)