Question

A pair of fair dice is cast. What is the probabiliy that the sum of the numbers falling uppermost is 9, given that at least one of the numbers falling uppermost is a 3?

a) 0.0556

b) 0.3056

c) 0.1818

d) 0.1111

e) 0.5000

f) None of the above.

Two cards are drawn without replacement from a well-shuffled deck of 52 playing cards. What is the probability that the first card drawn is a 2 and the second card drawn is a 3?

a) 0.1554

b) 0.0045

c) 0.0060

d) 0.0059

e) 0.1569

f) None of the above.

Answer 1

1. There are 36 possible outcomes when two dice are cast. The outcomes that give a sum of 9 are given below:

(3,6), (4,5), (5,4), (6,3) = 4 outcomes

The outcomes in which at least one number is a 3 are:

(1,3), (2,3), (3,1), (3,2), (3,3), (3,4), (3,5), (3,6), (4,3), (5,3), (6,3) = 11 outcomes

Outcomes in which sum is 3 and at least one number is 3 = (3,6), (6,3) = 2 outcomes

P(sum is 9 | at least one number is 3) = Number of outcomes in which sum is 3 and at least one number is 3 / Number of outcomes in which at least one number if 3

= 2/11

= 0.1818

2. Number of 2s = 4

Number of 3s = 4

P(first card is 2 and second card is 3) = 4/52 x 4/51

= 0.0060