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3847

2021-01-07 Binomial distribution shark 1 min read

Aja’s favorite cereal is running a promotion that says 1-in-4 boxes of the cereal contain a prize. Suppose that Aja is going to buy 5 boxes of this cereal, and let $X$ represent the number of prizes she wins in these boxes. Assume that these boxes represent a random sample, and assume that prizes are independent between boxes.

What is the probability that she wins at most 1 prize in the 5 boxes?
You may round your answer to the nearest hundredth.

$P(X \leq 1) = ?$

0.63

Solution:

(1) $\begin{align*}P(X \leq 1) & = P(X=0) + P(X=1) \\& = (\frac{3}{4})^5 + \frac{1}{4} \times (\frac{3}{4})^4 \times 5 \\& = 0.63\end{align*}$

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