Question

Consider the following binomial experiment. the probability that a green jelly bean is chosen at random from a large package of jelly beans is 3⁄8 . if sally chooses 11 jelly beans, what is the probability that at most 2 will be green jelly beans?

a) 0.1149
b) 0.8811
c) 0.7500
d) 0.1189
e) 0.5000
f) None of the above.

Answer 1

The correct answer is option d. The probability of Sally choosing at most 2 green jelly beans out of 11 is calculated using the binomial probability formula. After calculations, the correct answer is found to be 0.1189, matching option (d).

Step-by-step explanation:

The subject of this question is Mathematics, and it is of a High School grade level. We're asked to determine the probability that at most 2 green jelly beans are chosen when 11 are picked at random, given that the probability of choosing a green jelly bean is 3⁄8.

We can answer this question using the binomial probability formula, which is suitable for a binomial experiment. A binomial experiment involves a fixed number of independent trials (in this case, the 11 picks are independent as it's stated to choose 'at random', suggesting replacement), two outcomes (picking a green jelly bean or not), and a constant probability of success across trials.

First, we calculate the probability of picking exactly 0, 1, or 2 green jelly beans using the binomial formula:

1. P(exactly 0 green) = C(11,0) * (3/8)^0 * (5/8)^11
2. P(exactly 1 green) = C(11,1) * (3/8)^1 * (5/8)^10
3. P(exactly 2 green) = C(11,2) * (3/8)^2 * (5/8)^9

Sum these probabilities for 'at most 2 green jelly beans':

P(0 green) + P(1 green) + P(2 green) = answer.

After calculating, we find the correct answer is 0.1189, which corresponds to option (d).