The probability that a house in an urban area will develop a leak is 55 %. if 2020 houses are randomly selected, what is the probability that none of the houses will develop a leak? round to the nearest thousandth.

The probability that a house in an urban area will develop a leak is 55 %. if 20 houses are randomly selected, what is the probability that none of the houses will develop a leak? round to the nearest thousandth.

Use binomial distribution, since probability of developing a leak, p=0.55 is assumed constant, and

n=20, x=0

and assuming leaks are developed independently between houses,

P (X=x)

=C (n, 0) p^x * (1-p) ^ (n-x)

=C (20,0) 0.55^0 * (0.45^20)

=1*1*0.45^20

=1.159*10^ (-7)

=0.000