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

Relevance
  • 1 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

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