Question

A pair of fair dice is rolled. What is the probability of each of the following? (Round your answers to three decimal places.)
(a) the sum of the numbers shown uppermost is less than 5
and
(b)at least one 5 is cast

Answer 1

SOLUTION :

(a)

Pair of dice are rolled.

P(Sum < 5 ) 

= P(Sum = 2) + P(Sum = 3) + P(Sum = 4)

= P(1, 1) + P(1,2) + P(2,1) + P(1, 3) + P(2, 2) + P(3, 1)

P(each outcome) = 1/36 , total outcomes = 6

Hence.

P(Sum < 5) = 6 * 1/36 = 1/6 (ANSWER).

(b)

P(at least one 5 is cast)

= P(5, Not 5) + P( Not 5, 5)

= (1/6 * 5/6) +  (5/6 * 1/6)

= 5/36 + 5/36

= 5/18 (ANSWER).