Market research has shown that $60\%$ of the customers at an electronics store opt to pay for

Question

Market research has shown that $60\%$ of the customers at an electronics store opt to pay for their purchases by instalments. There are $24$ customers at the electronics store on a particular morning. Find the probability that the ${{8}^{\mathrm{th}}}$ customer to the store is the ${{4}^{\mathrm{th}}}$ customer who opts to pay for his purchase by instalments and there are less than $10$ customers opting to pay by instalments. Find the least value of $n$ such that the probability that the $n$ th customer to the store is the ${{4}^{\mathrm{th}}}$ customer opting to pay by instalments is at most $0.12$. There are $k$ customers at the electronics store on a particular afternoon. Find the least value of $k$ such that the probability of at most $(k-2)$ customers not opting to pay by instalments is more than $0.99$.

Accepted Answer

(i) $0.00222$ (ii) $8$ if $n\geq4$ is intended; literally $1$ if all positive integers are allowed (iii) $8$

Discrete Random Variables (DRV) - Binomial Probabilities Using the Probability Mass Function

Discrete Random Variables (DRV) - Binomial Probabilities Using the Probability Mass Function

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