Question

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.

Answer 1

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