# Лекция: Exercises (using conditional probability)

1. For two events A and B it is given that and P(A|B)=. Find

a)

b)

2. A bag contains 6 balls, each with a number between 4 and 9 written on it. Each ball has a different number written on it. Find the probability that if two balls are drawn

a) the sum of the scores is greater than 12

b) the second ball shows a 7, given that the sum of the scores is greater than 12

c) the first ball is even, given that the difference between the numbers is 3.

3. In a game of Scrabble, Dalene has the seven letters A, D, E, K, O, Q and S. She picks two of these letters at random.

a) What is the probability that one is a vowel and the other is the letter D?

b) If the first letter she picks is a consonant, what is the probability that the second letter is the E?

c) Given that she picks the letter Q first, what is the probability that she picks the letter D or the letter K second?

4. There are ten discs in a bag. Each disc has a number on it between 0 and 9. Each number only appears once. Hamish picks two discs at random. Given that the first disc drawn shows a multiple of 4, what is the probability that

a) the sum of the numbers on the two discs is less than10

b) the sum of the numbers on the two discs is even

c) the difference between the two numbers on the discs is less than 3?

5. On any given day in June the probability of it raining is 0.24. The probability of Suzanne cycling to work given that it is raining is 0.32. Find the probability that Suzanne cycles to work and it is raining.

6. Events A and B are such that and The conditional probability

a) Find .

b) Are A and B exhaustive events? Give a reason for the answer.

7. The probability of Nick gaining a first class degree at university given that he does 25 hours revision per week is 0.7. The probability that he gains a first class degree and does 25 hours revision per week is 0.85. Find the probability that he does 25 hours revision.