You are told that 90% of homes donate to your charitable cause. You have 46 tax

Question

You are told that 90% of homes donate to your charitable cause. You have 46 tax receipts left and plan on canvassing a neighbourhood having 50 homes (assume that each home making a donation will want a tax receipt).

a) What is the expected number of homes in this neighbourhood who will make a donation?

b) What is the probability that you will not run out of receipts before finishing canvasing the neighbourhood?

c) What is the probability that you will have receipts left over when you finish canvassing the neighbourhood?

d) A friend informs you that at least one home in the neighbourhood will not make a donation.If your friends information is correct, what now is the probability that you will have enough receipts to canvas the neighbourhood?

answer

45

0.7497

0.5688

0.75358

Explanation / Answer

Solution:-

a) The expected number of homes in this neighbourhood who will make a donation is 45

E(x) = 0.90 × 50

E(x) = 45

b) The probability that you will not run out of receipts before finishing canvasing the neighbourhood is 0.7497.

x = 46, n = 50, p = 0.90

By applying binomial distributiion:-

P(x,n) = nCx*px*(1-p)(n-x)

P(x < 46) = 0.7497

c) The probability that you will have receipts left over when you finish canvassing the neighbourhood is 0.569.

x = 46, n = 50, p = 0.90

By applying binomial distributiion:-

P(x,n) = nCx*px*(1-p)(n-x)

P(x < 46) = 0.569

d) Now is the probability that you will have enough receipts to canvas the neighbourhood is 0.8799.

x = 46, n = 49, p = 0.90

By applying binomial distributiion:-

P(x,n) = nCx*px*(1-p)(n-x)

P(x < 46) = 0.8799

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