a) A probability tree diagram is drawn.
b) The probability of being late for school is: 7/30.
c) The probability that he will be late for school if he does not use a matatu is 1/10.
What is the probability?
a) A probability tree diagram representing the given information:
_______1/3_______
/ \
/ \
Bus (1/5) Matatu (3/10)
/ \
/ \
Late (1/20) Late (1/20)
b) To find the probability that he will be late for school, we need to consider all the possible paths that lead to being late.
The probability of taking a bus and being late is (1/3) * (1/5) = 1/15.
The probability of taking a matatu and being late is (1/2) * (3/10) = 3/20.
The probability of taking other means of transport and being late is:
(1 - 1/3 - 1/2) * (1/20) = 1/20.
Therefore, the total probability of being late for school is:
1/15 + 3/20 + 1/20 = 7/30.
c) To find the probability that he will be late for school if he does not use a matatu, we need to consider the paths that do not involve a matatu.
The probability of taking a bus and being late is (1/3) * (1/5) = 1/15.
The probability of taking other means of transport and being late is (1 - 1/3) * (1/20) = 2/60 = 1/30.
Therefore, the total probability of being late for school if he does not use a matatu is:
1/15 + 1/30 = 3/30 = 1/10.
So, the probability that he will be late for school if he does not use a matatu is 1/10.
Complete question is:
The probability that a boy goes to school by bus is ⅓ and by matatu is ½.If he uses a bus,the probability that he is late to school is 1/5 and if he uses a matatu,the probability of being late is 3/10.If he uses other means of transport,the probability of being late is 1/20.
a)Draw a probability tree to represent this information.
b)What is the probability that he will be late for school?
c) What is the probability that he will be late for school if he does not use a matatu?