Question

trial outcome
1 41985
2 07738
3 38869
4 61941
5 41466
6 33325
7 52644
8 52348
9 82462
10 66233
11 81692
12 14702
13 03848
14 73032
15 36656
res in 80% of his games. they are starting the playoffs and if they make it to the state championship, they will have 5 games. joel wants to determine the probability that he scores in exactly 4 of the 5 games.

Explanation:

Step1: Identify distribution parameters

We use the binomial distribution: $n=5$ (total games), $k=4$ (successes), $p=0.8$ (win probability)

Step2: Apply binomial formula

Binomial probability: $P(X=k)=\binom{n}{k}p^k(1-p)^{n-k}$
$\binom{5}{4}=\frac{5!}{4!(5-4)!}=5$

Step3: Calculate each component

$p^k=0.8^4=0.4096$, $(1-p)^{n-k}=(0.2)^1=0.2$

Step4: Compute final probability

$P(X=4)=5\times0.4096\times0.2=0.4096$

Answer:

0.4096