Question

1. Suppose the probability that a library patron checks out a science fiction book is 0.08.

What is the probability that 3 of the next 12 library patrons will sign out a science fiction book? = 0.0532

What is the probability that none of the next 10 patrons sign out a science fiction book? =0.4344

What is the probability that at least one patron will sign out a science fiction book? = ??????????

Answer 1

a)

X ~ bin (n , p)

Where n = 12 , p = 0.08

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

P(X = 3) = ¹²C₃ * 0.08³ * ( 1 - 0.08)⁹

= 0.0532

b)

For n = 10

P(X = 0) = ¹⁰C₀ * 0.08⁰ * ( 1 - 0.08)¹⁰

= 0.4344

c)

P(X >= 1 ) = 1 - P(X = 0)

= 1 - 0.4344

= 0.5656