Question

Suppose you toss a six-sided die 10 times. What is the probability of never rolling a 4?

Answer 1

Let Y denotes the number of events of getting 4 in the roll of six-sided die 10 times. The random variable Y follows binomial distribution with parameters N = 10 and p = 1 / 6.

The probability distribution of Y is given as $\dpi{100} \small P\left ( Y=y \right )=10C_{y}\left ( 1/6 \right )^{y}(5/6)^{10-y}$ for y = 0, 1, ... 10.

Probability of never rolling a 4 in tossing six-sided die 10 times is given as

$\dpi{100} \small P\left ( Y=0 \right )=10C_{0}\left ( 1/6 \right )^{0}(5/6)^{10-0}=\left ( 5/6 \right )^{10}=0.162$

Probability of never rolling a 4 in tossing six-sided die 10 times is 0.162.