# statistics problem.....?

All holy plants are dioecious-a male plant must be planted within 30 to 40 feet of the female plant in order to yield barriers. A home improvement store has 12 unmarked holly plants for sale, 8 of which are female. If a homeowner buys 4 plants at random, what is the probability that berries will be produced?

Relevance

We assume that all the plants will be planted within the required distance.

So of the 4 plants chosen, at least 1 and at most 3 must be male. This is a hypergeometric distribution problem. You have to calculate the probabilities for each of 1, 2, and 3 male plants, OR, a little easier, calculate the probability of 0 males and 4 males and subtract them from1, because those are the probabilities of failing.

The general formula for the probability of r successes in a sample of size n, from a population of size N, with k "marked" members is

P(x = r) = [kCr * (N-k)C(n-r)]/(NCn)

Where N = 12, n = 4, k = 4, N-k = 8, and r = 0 in one case and r = 4 in the other.

For r = 0, this reduces to

8C4/12C4 = .141414

For r = 4, it reduces to

4C4/12C4 = 1/12C4 = .00202

So the probability of NOT getting any berries is about .14316, and the probability of getting berries is 1 minus that probability.

• Anonymous
6 years ago

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