A fair die is rolled 10 times.What is the probability that an odd number (1,3,or 5)will occur less than 3 times?
A).0547
B).1172
C).1550
D).7752
E).8450

Question

Quizplus · Accepted Answer

The probability of rolling an odd number on a fair die is 3/6 or 1/2. The probability of rolling an odd number less than 3 times in 10 rolls can be calculated by finding the probability of rolling 0, 1, or 2 odd numbers.

P(0 odds) = (1/2)^10 = 1/1024
P(1 odd) = 10*(1/2)^10 = 10/1024
P(2 odds) = 45*(1/2)^10 = 45/1024

Therefore, P(less than 3 odds) = P(0 odds) + P(1 odd) + P(2 odds) = 1/1024 + 10/1024 + 45/1024 = 56/1024 = 0.0547.

Option A) is the closest choice to this probability.

A Fair Die Is Rolled 10 Times