A very large gardening business grows rose bushes for sale to garden stores around the world. The most popular colors are red, pink, and white. The business decides on 50% red roses, 30% pink, and 20% white. A gardener orders 10 rose bushes selected randomly from a huge field. Her primary interest is in pink roses. Assuming rose bushes are selected independently, we can use the binomial distribution for calculations. The probability of getting at least 3 pink rose bushes is:

Question

Quizplus · Accepted Answer

The probability of getting a pink rose is 0.3. 
The probability of getting at least 3 pink roses can be calculated using the binomial distribution formula:
P(X≥3) = 1 - P(X<3)
= 1 - [P(X=0) + P(X=1) + P(X=2)]
= 1 - [(10 choose 0) * (0.3)^0 * (0.7)^10 + (10 choose 1) * (0.3)^1 * (0.7)^9 + (10 choose 2) * (0.3)^2 * (0.7)^8]
= 1 - [0.028 + 0.121 + 0.233]
= 0.617 
Therefore, the probability of getting at least 3 pink roses is 0.617, which is option B.

A Very Large Gardening Business Grows Rose Bushes for Sale