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
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
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
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
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
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
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
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. 
(c) Find the probability that on any given day:
(i) Gataro plays football; (ii) Gataro neither jogs nor plays football.
answers
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
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
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.
aNSWER
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
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
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
Form 3 MathematicsDuring 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:-
Answer
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