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.)
Accepted Solution
A:
Answer: 0.01708Step-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 : [tex]p=\dfrac{15}{1000}=0.015[/tex]The formula for binomial distribution is given by :-[tex]^{n}C_xp^x(1-p)^{n-x}[/tex]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[tex]^{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[/tex]Hence, the required probability = 0.01708