7. An urn contains four black and eight white balls. A sample of five balls is...

Question

Question

Answer 1

Answer #1

a) here as probability of a white ball =8/12=2/3

therefore from binomial distribution P(X<=2)=P(X=0)+P(X=1)+P(X=2)

=⁵C₀(2/3)⁰(1/3)⁵+⁵C₁(2/3)¹(1/3)⁴+⁵C₂(2/3)²(1/3)³=0.209877

b)

this follows geometric distribution with parameter p=0.209877

expected selections =1/p=1/0.209877=4.76

c)

P(first time on 10th selection)=P(not happened for first 9 time and happens on 10th time)=(1-0.209877)⁹*(0.209877)

=0.025189

d)

Probability=P(E happens exactly 9 times in first 59 selection and happens on 60th selection)

=⁵⁹C₉(0.209877)⁹*(1-0.209877)=0.01598

e)

this follows negative binomial with paramter n=10 and p=0.209877

expected number =r/p=10/0.209877=47.64696

Answer 2

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