The probability that a house in an urban area will develop a leak is 2%. If 21 houses are randomly selected, what is the probability that none of the houses will develop a leak?

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:

Thus, the probability that none of the houses will develop a leak is 0.6543.

first option

a function is a relation in which an input is paired with exactly one output.

so, let's find the right answer.

in our first option, our inputs are january, february, and march. the outputs are 30, 28, and 25. each input has it's own output. this is correct!

our second option we know is incorrect, because ms. valverade has two outputs, dogs and cats. this is not a function.

our third option is incorrect as well. the yellow square has two ouputs, the square and the triangle.

lastly, in our fourth option, we see the number 7 two times with a different output. therefore, this is not a function.

remember: each input must be paired with only one output!