Question

What is the probability that the San Jose Sharks win at least five games in that upcoming month

$a.0.3694b.0.5266c.0.4734d.0.2305$

Short answer

b.$0.5266$

Step-by-step solution

Given information

Given that
San Jose sharks will win any given game is$0.3694$
$$\begin{gathered} P=0.3694 \\ (1-P)=1-0.3694=0.6306 \end{gathered}$$
The upcoming month schedule contains 12 games .$\left(n\right)=12$

Explanation

We know that
Binomial Probability

Probability that San Jose Sharks will win 5 games in the upcoming month. $=P(X<5)$
Here,
$n=12,x=0,P=0.3694$
Then binomial probability

$P\left(X\right)=\frac{n!}{X!(n-X)!}\cdot p^X\cdot (1-p{)}^{n-X}$

$P\left(0\right)=\frac{12!}{0!(12-0)!}\cdot {0.3694}^0\cdot (1-0.3694{)}^{12-0}$

$P\left(0\right)=0.0039540995304692$

To calculate any remaining probabilities, we need to either use the binomial probability distribution function on a calculator or the binomial probability formula. We'll add these remaining probabilities to P(0) for our final answer.

$\begin{array}{c}P\left(0\right)+P\left(1\right)+P\left(2\right)+P\left(3\right)+P\left(4\right)\\ 0.0039540995304692+0.027795325719416+0.089552431436945+0.17486345370973+0.23047535609078\\ =0.52664066648735\end{array}$

The probability to win at least five games in that upcoming month is$0.5266$