Лекция: Exercises (using probability of compound events)
1 Sheila is picking books off her shelf. The shelf only contains mathematics books and novels. The probability that she picks a novel is 0.48 and the probability that she picks a mathematics book is 0.52.
a) What is the probability that she does not pick a mathematics book?
b) Explain why these events are exhaustive.
2 If are A and B exhaustive events?
3 The probability that Hanine goes to the local shop is The probability that she does not cycle is The probability that she goes to the shop and cycles is
a) What is the probability that she cycles?
b) What is the probability that she cycles or goes to the shop?
4 It is given that for two events A and B, and Find P(B).
5 In a class, 6 students have brown eyes, 3 students have blue eyes, 4 students have grey eyes and 2 students have hazel eyes. A student is chosen at random. Find the probability that
a) a student with blue eyes is chosen
b) a student with either blue or brown eyes is chosen
c) a student who does not have hazel eyes is chosen
d) a student with blue, brown or grey eyes is chosen
e) a student with grey or brown eyes is chosen.
6 Two tetrahedral dice are thrown. What is the probability that
a) the sum of the two scores is 5
b) the sum of the two scores is greater than 4
c) the difference between the two scores is 3
d) the difference between the two scores is less than 4
e) the product of the two scores is an even number
f) the product of the two scores is greater than or equal to 6
g) one die shows a 3 and the other die shows a number greater than 4?
7 Two cubical dice are thrown. What is the probability that
a) the sum of the two scores is 9
b) the sum of the two scores is greater than 4
c) the difference between the two scores is 3
d) the difference between the two scores is at least 4
e) the product of the two scores is 12
f) the product of the two scores is an odd number
g) one die shows an even number or the other die shows a multiple of 3?
8 The probability that John passes his mathematics examination is 0.9, and the probability that he passes his history examination is 0.6. These events are exhaustive. What is the probability that
a) he does not pass his mathematics examination
b) he passes his history examination or his mathematics examination
c) he passes his mathematics examination and his history examination?
9 In a school’s IB diploma programme, 30 students take at least one science. If 15 students take physics and 18 students take chemistry, find the probability that a student chosen at random studies both physics and chemistry.
10 There are 20 students in a class. In a class survey on pets, it is found that 12 students have a dog, 5 students have a dog and a rabbit and 3 students do not have a dog or a rabbit. Find the probability that a student chosen at random will have a rabbit.
11 In a survey of people living in a village, all respondents either shop at supermarket A, supermarket B or both. It is found that the probability that a person will shop at supermarket A is 0.65 and the probability that he/she will shop at supermarket B is 0.63. If the probability that a person shops at both supermarkets is 0.28, find the probability that a person from the village chosen at random will shop at supermarket A or supermarket B, but not both.
12 Two cubical dice are thrown. What is the probability that the sum of the two scores is
a) a multiple of 3
b) greater than 5
c) a multiple of 3 and greater than 5
d) a multiple of 3 or greater than 5 e less than 4 or one die shows a 5?
e) Less than 4 or one die shows a 5?
f) Explain why the events in part eare mutually exclusive.
13 A class contains 15 boys and 17 girls. Of these 10 boys and 8 girls have blonde hair. Find the probability that a student chosen at random is a boy or has blonde hair.
14 Two tetrahedral dice are thrown. What is the probability that the sum of the scores is
a) even
b) prime
c) even or prime?
d) Explain why these two events are mutually exclusive.
15 When David goes fishing the probability of him catching a fish of type A is 0.45, catching a fish of type B is 0.75 and catching a fish of type C is 0.2. David catches four fish. If the event X is David catching two fish of type A and two other fish, the event Y is David catching two fish of type A and two of type B and the event Z is David catching at least one fish of type C, for each of the pairs of X, Y and Z state whether the two events are mutually exclusive, giving a reason.
16 If A and B are exhaustive events, and and find
17 A whole number is chosen from the numbers 1 to 500. Find the probability that the whole number is
a) a multiple of 6
b) a multiple of both 6 and 8.