Question

A gardener has fourteen identical looking tulip bulbs, of which seven will produce

yellow tulips and seven will become pink. She randomly selects and plants six of
them and then gives the rest away. When the flowers start to bloom, what is the
probability that at least two of them are yellow?
73.81%
94.872%
52.914%
89.977%

Answer 1

To find the probability that at least two of the flowers are yellow when 6 bulbs are randomly selected and planted, we need to calculate the probabilities of getting exactly 2, 3, and 4 yellow bulbs. With these probabilities, we can determine the final answer. The probability is found to be 86.328%.

Step-by-step explanation:

In this scenario, the gardener has a total of 14 tulip bulbs, with 7 of them producing yellow tulips and 7 producing pink tulips. The gardener randomly selects and plants 6 bulbs.

To find the probability that at least two of the flowers are yellow, we need to calculate the probability of getting exactly 2 yellow bulbs, exactly 3 yellow bulbs, and exactly 4 yellow bulbs. We can then sum up these probabilities to find the final answer.

Using the combination formula, the probability of getting exactly x yellow bulbs out of 6 can be calculated as:

P(x yellow bulbs) = C(7, x) * C(7, 6 - x) / C(14, 6)

Plugging in the values, we find:

P(2 yellow bulbs) = C(7, 2) * C(7, 4) / C(14, 6) = 0.390625

P(3 yellow bulbs) = C(7, 3) * C(7, 3) / C(14, 6) = 0.317708

P(4 yellow bulbs) = C(7, 4) * C(7, 2) / C(14, 6) = 0.154947

Finally, summing up these probabilities gives us:

P(at least two yellow bulbs) = P(2 yellow bulbs) + P(3 yellow bulbs) + P(4 yellow bulbs) = 0.390625 + 0.317708 + 0.154947 = 0.86328 = 86.328%