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?
- FlashRubinoLv 66 years agoFavorite Answer
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.
- Anonymous6 years ago
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