Question

A fair 6-sided die rolled 5 times. what is the probability that at least one of the rolls is 2

Answer 1

Solution :

A fair 6-sided die rolled 5 times.

Probability of getting a 2 on throwing a single dice = (1/6)

Probability of not getting a 2 on throwing a single dice = 1 - (1/6) = 5/6

Probability of obtaining zero 2's on rolling a fair dice 5 times is given by,

$P(not\ 2) = \left ( \frac{5}{6} \right )^{5}$

Hence, probability of obtaining at least one of the 2 on rolling a fair dice 5 times is given by,

$P(at\ least\ one\ 2) = 1- \left ( \frac{5}{6} \right )^{2}$

The probability that at least one of the rolls is 2 is 0.5981.