Answer :
Answer:
The probability that n of the cars tested turn out to be lemons is [tex]{m\choose n}\times\frac{k^{m}(100-k)^{(m-n)}}{100^{m}}[/tex].
Step-by-step explanation:
Let X = a car is lemon
There are 100 cars in a parking lot.
The probability that a car is a lemon is:
[tex]P (A\ car\ is\ lemons) = \frac{Number\ of\ cars\ that\ are\ lemons}{Total\ number\ of\ cars} =\frac{k}{100}[/tex]
The random variable [tex]X\sim Bin (100, \frac{k}{100})[/tex]
The probability function of a Binomial distribution is:
[tex]P(X=a)={a\choose b}\times p^{b}\times (1-p)^{a-b}[/tex]
Number of cars selected is a = m.
Compute the probability that out of m cars n turn out to be lemons as follows:
[tex]P(X=n)={m\choose n}\times [\frac{k}{100}] ^{n}\times (1-\frac{k}{100} )^{m-n}={m\choose n}\times\frac{k^{m}(100-k)^{(m-n)}}{100^{m}}[/tex]
Thus, the probability that out of m cars n turns out to be lemons is [tex]{m\choose n}\times\frac{k^{m}(100-k)^{(m-n)}}{100^{m}}[/tex].
