the probability that a house in an urban area will develop a leak is 5%. if 23 houses are randomly selected, what is the probability that none of the houses will develop a leak?
Try the binomial distribution.
Here is the formula:
P(x) = (nCx)(p^x)[q^(n-x)]
x = 0
p = .05
n = 23
Substitute into the formula to determine the probability.
Note: q = 1 - p
0.000001
Well, I must say, these houses sure know how to keep themselves dry! Now, let's calculate the probability.
The probability of a house developing a leak is 5% or 0.05. Therefore, the probability of a house not developing a leak is 1 - 0.05, which is 0.95.
Now, if we want to find the probability that none of the 23 houses will develop a leak, we multiply the probabilities of each individual house not developing a leak. So, it would be 0.95 raised to the power of 23.
Using my wit and a calculator, I can tell you that the probability comes out to be approximately 0.358491. So, there's a 35.85% chance that none of these houses will develop a leak! Keep those faucets in check, folks! 🤡
To find the probability that none of the houses will develop a leak, we can use the concept of independent events. Since each house selected is an independent event and the probability of a house developing a leak is 5%, we can calculate the probability of none of the selected houses developing a leak.
The probability of a house not developing a leak is the complement of the probability of a house developing a leak, which is 1 - 0.05 = 0.95.
Now, to find the probability that none of the 23 houses will develop a leak, we multiply the probabilities of each independent event. Since all events are assumed to be independent, we multiply the probability of a house not developing a leak (0.95) by itself 23 times.
P(none of the 23 houses will develop a leak) = (0.95)^23
Using a calculator, we can compute this probability:
P(none of the 23 houses will develop a leak) ≈ 0.3585
Therefore, the probability that none of the 23 houses will develop a leak is approximately 0.3585 (or 35.85%).