To find the probability that at least 10 pineapples in a case of 12 are ripe within four days, we can use the binomial probability formula:
P(X >= 10) = P(X = 10) + P(X = 11) + P(X = 12)
Where:
- P(X = x) is the probability of x successes in n trials, given by the formula C(n, x) * p^x * (1-p)^(n-x)
- n = 12 (number of pineapples in the case)
- p = 0.92 (probability that a pineapple will ripen within four days)
- C(n, x) is the number of ways to choose x successes out of n trials, given by the formula n! / (x! * (n-x)!)
Now we can calculate the individual probabilities:
P(X = 10) = C(12, 10) * 0.92^10 * (1-0.92)^(12-10) = 0.349
P(X = 11) = C(12, 11) * 0.92^11 * (1-0.92)^(12-11) = 0.328
P(X = 12) = C(12, 12) * 0.92^12 * (1-0.92)^(12-12) = 0.268
Now, add these probabilities together:
P(X >= 10) = 0.349 + 0.328 + 0.268 = 0.945
Therefore, the probability that at least 10 pineapples in a case of 12 are ripe within four days is 0.945 or 94.5%.
A fruit company guarantees that 92% of the pineapples it ships will ripen within four days of delivery. Find the probability that at least 10 pineapples in a case of 12 are ripe within four days.
3 answers
wrong
I apologize for the error in the previous response. Let's correct it:
To find the probability that at least 10 pineapples in a case of 12 are ripe within four days, we can calculate the probability of exactly 10 ripe pineapples, 11 ripe pineapples, or 12 ripe pineapples and then sum them up.
Let's calculate each separately:
1. Probability of exactly 10 ripe pineapples:
P(X = 10) = C(12, 10) * (0.92)^10 * (0.08)^2 = 0.3512
2. Probability of exactly 11 ripe pineapples:
P(X = 11) = C(12, 11) * (0.92)^11 * (0.08)^1 = 0.3824
3. Probability of exactly 12 ripe pineapples:
P(X = 12) = C(12, 12) * (0.92)^12 * (0.08)^0 = 0.2598
Now, add these probabilities together:
P(X >= 10) = P(X = 10) + P(X = 11) + P(X = 12)
P(X >= 10) = 0.3512 + 0.3824 + 0.2598
P(X >= 10) = 0.9934
Therefore, the correct probability that at least 10 pineapples in a case of 12 are ripe within four days is 0.9934 or 99.34%.
To find the probability that at least 10 pineapples in a case of 12 are ripe within four days, we can calculate the probability of exactly 10 ripe pineapples, 11 ripe pineapples, or 12 ripe pineapples and then sum them up.
Let's calculate each separately:
1. Probability of exactly 10 ripe pineapples:
P(X = 10) = C(12, 10) * (0.92)^10 * (0.08)^2 = 0.3512
2. Probability of exactly 11 ripe pineapples:
P(X = 11) = C(12, 11) * (0.92)^11 * (0.08)^1 = 0.3824
3. Probability of exactly 12 ripe pineapples:
P(X = 12) = C(12, 12) * (0.92)^12 * (0.08)^0 = 0.2598
Now, add these probabilities together:
P(X >= 10) = P(X = 10) + P(X = 11) + P(X = 12)
P(X >= 10) = 0.3512 + 0.3824 + 0.2598
P(X >= 10) = 0.9934
Therefore, the correct probability that at least 10 pineapples in a case of 12 are ripe within four days is 0.9934 or 99.34%.