Question

Suppose the probability that a library patron checks out a love book is 0.08.

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

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

The answer is NOT 0.5656, 0.6323, 0.08

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

Answer 1

Let X denotes the number of library patrons who will sign out a love book in a random sample of 12 library patrons.

Here,

X ~ Binomial(n = 12, p = 0.08)

The probability mass function of X is

Now,

i) The probability that 3 of the next 12 library patrons will sign out a love book

ii) The probability that at least one patron will sign out a love book

It will be 0.6323 if sample size = 12 for this too.

Let Y denotes the number of library patrons who will sign out a love book in a random sample of 10 library patrons.

Here,

Y ~ Binomial(n = 10, p = 0.08)

The probability mass function of Y is

Now,

The probability that none of the next 10 patrons sign out a love book