The general life-span of an insect is 7-9 months. What is the probability that the insect will die in exactly 7 months?

To calculate the probability that the insect will die in exactly 7 months, we need to know the total lifespan of the insect and the probability of dying in each month.

Given that the general lifespan of the insect is 7-9 months, we can assume that the insect has an equal probability of dying in each of these months. Therefore, the probability of dying in any given month is 1/3.

To find the probability of dying in exactly 7 months, we can use the binomial probability formula. The formula is:

P(X=k) = (nCk) * p^k * (1-p)^(n-k)

Where: P(X=k) is the probability of exactly k successes (in this case, dying in exactly 7 months) n is the total number of trials (in this case, the total lifespan of the insect, which is 9 months) k is the number of successful trials (in this case, dying in 7 months) p is the probability of success in a single trial (in this case, the probability of dying in any given month, which is 1/3)

Plugging in the values, we have:

P(X=7) = (9C7) * (1/3)^7 * (2/3)^(9-7)

Calculating this expression will give us the probability that the insect will die in exactly 7 months.