Find the probability.
-A child rolls a 6-sided die 6 times. What is the probability of the child rolling exactly four fives? Round to the nearest ten-thousandth.
A) 0.5360
B) 0.0080
C) 0.3125
D) 0.9688

Question

Find the probability.
-A child rolls a 6-sided die 6 times. What is the probability of the child rolling exactly four fives? Round to the nearest ten-thousandth.
A) 0.5360
B) 0.0080
C) 0.3125
D) 0.9688

Quizplus · Accepted Answer

The probability of rolling exactly four fives in six rolls of a 6-sided die can be calculated using the binomial probability formula, which is $P(X=k) = \binom{n}{k}p^k(1-p)^{n-k}$, where $n$ is the number of trials, $k$ is the number of successful outcomes, $p$ is the probability of success on a single trial, and $\binom{n}{k}$ is the binomial coefficient. Here, $n=6$, $k=4$, and $p=\frac{1}{6}$ (since there's one five on a 6-sided die). Plugging these values into the formula gives a probability of approximately 0.0080.

Find the Probability. -A Child Rolls a 6-Sided Die 6 Times. What Is