# Statistics?

A sport commentator claims that 45% of all football injuries are knee injuries are knee injuries. If this claims is true. What is the probability that in a game with 5 reported injuries

at least is a knee injury ?

exactly 3 arre knee injuries?

more than 2 are knee injuries?

none are 2 knee injuries?

### 1 Answer

- paramvenuLv 71 month ago
p = 45% or 0.45

q = 1-p = 1-0.45 = 55

n = 5

According to Binomial distribution

P(x) = Cx*p^x*q^(n-x)

i) At least 1

Required probability = P(x >/= 1)

= 1 - P(x=0)

= 1 - 5C0*0.45^0*0.55^5

= 1 - 0.0503

= 0.9497

ii) Exactly 3

Required probability = P(x=3)

= 5C3*0.45^3*0.55^2

= 0.2757

iii) More than 2

Required probability = P(x > 2)

= P(x=3)+P(x=4)+P(x=5)

= 5C3*0.45^3*0.55^2 + 5C4*0.45^4*0.55^1 + 5C5*0.45^5*0.55^0

= 0.2757 + 0.1128 + 0.0185

= 0.4070

iv) None

Required Probability = P(x=0)

= 5C0*0.45^0*0.55^5

= 0.0503