Question

If records indicate that 15 houses out of 1000 are expected to be damaged by fire in any year, what is the probability that a woman who owns 14 houses will have fire damage in 2 of them in a year? (Round your answer to five decimal places.)

Answer 1

Answer: 0.01708

Step-by-step explanation:

Given : If records indicate that 15 houses out of 1000 are expected to be damaged by fire in any year.

i.e. the probability that house damaged buy fire in a year : $p=\dfrac{15}{1000}=0.015$

The formula for binomial distribution is given by :-

$^{n}C_xp^x(1-p)^{n-x}$

Now, the probability that a woman who owns 14 houses will have fire damage in 2 of them in a year (put n=14 and x=2), we get

$^{14}C_2(0.015)^2(1-0.015)^{14-2}\\\\=\dfrac{14!}{2!(14-2)!}(0.015)^2(0.985)^{12}\\\\=0.0170788520518\approx0.01708$

Hence, the required probability = 0.01708