Question

A collegiate video-game competition team has a 0.65 probability of winning a match. Over the course of a season, 12 matches are played. Individual matches are independent of any other matches. Calculate the probability that the team will win exactly 6 matches over the course of one season. [ENTER ANSWER TO 4 DECIMAL PLACES, e.g. a 75% probability would be entered as "0.7500"]

Answer 1

Given:

A collegiate video-game competition team has a 0.65 probability of winning a match. Over the course of a season, 12 matches are played.

Probability of winning match, p= 0.65

Number of trials, n= 12

Let X : The team will win matches over the course of one season.

X follows the Binomial Distribution.

X ~ Binomial(n=12, p = 0.65)

The probability function of Binomial Distribution is given by

P(X=x) = nCx * p^x * (1-p)^n-x

The probability that the team will win exactly 6 matches over the course of one season :

P(X=6) = 12C6 * (0.65)^6 * (1-0.65)^12-6

= 0.1281

Therefore the probability that the team will win exactly 6 matches over the course of one season is 0.1281