The probability that the san jose sharks will win any given game is 0.3694 based on a 13-year win history of 382 wins out of 1,034 games played (as of a certain date). an upcoming monthly schedule contains 12 games. what is the probability that the san jose sharks win at least 6 games in that upcoming month? let x = number of games won in that upcoming month. (round your answer to four decimal places.)

[tex]X[/tex] follows a binomial distribution [tex]\mathcal B(12,0.3694)[/tex]. We get

[tex]\mathbb P(X\ge6)=\displaystyle\sum_{x=6}^{12}p_X(x)[/tex]

where [tex]p_X(x)[/tex] is the PMF of the distribution given by

[tex]p_X(x)=\begin{cases}\dbinom{12}x0.3694^x(1-0.3694)^{12-x}&\text{for }0\le x\le12\\\\0&\text{otherwise}\end{cases}[/tex]

Using a calculator, you'd find

[tex]\mathbb P(X\ge6)\approx0.2573[/tex]