Answer :
Answer:
The probability that none of the houses will develop a leak is 0.6543.
Step-by-step explanation:
Let X denote the number of houses in an urban area that develop a leak.
The probability that a house in an urban area will develop a leak is, p = 0.02.
A random sample of n = 21 houses are selected.
Every house is independent of developing a leak.
Thus, the random variable X follows a binomial distribution with parameters n = 21 and p = 0.02.
Compute the probability that none of the houses will develop a leak as follows:
[tex]P(X=0)={21\choose 0}(0.02)^{0}(1-0.02)^{21-0}\\\\=1\times1\times 0.654256\\\\\approx 0.6543[/tex]
Thus, the probability that none of the houses will develop a leak is 0.6543.