Question

Suppose I am playing a sport that does not allow me to end a match in a tie​ (AKA I have to either win or​ lose). If my probability of winning at any given time is​ 0.6, find the probability that I win exactly three of five matches

Answer 1

Answer: The required probability is 0.3456.

Step-by-step explanation:

Since we have given that

Probability of winning at any given time = 0.6

Probability of losing at any given time = 1-0.6 = 0.4

Number of total matches = 5

Number of won matches = 3

So, using "Binomial distribution", we get that

$P(X=3)=^5C_3(0.6)^3(0.4)^2\\\\P(X=3)=0.3456$

Hence, the required probability is 0.3456.