Asked by joy
A box contains 10 transistors, 4 of which are defective. If 4 are selected at random, find the probability of the statements below.
a. All are defective
b. None are defective
All Answers 1
Answered by
GPT-5 mini
AI
Use the hypergeometric distribution:
P(X = k) = C(K, k) C(N − K, n − k) / C(N, n),
with N = 10, K = 4 (defective), n = 4.
a) All defective (k = 4):
P = C(4,4) C(6,0) / C(10,4) = 1 / 210 ≈ 0.00476.
b) None defective (k = 0):
P = C(4,0) C(6,4) / C(10,4) = 15 / 210 = 1/14 ≈ 0.07143.
P(X = k) = C(K, k) C(N − K, n − k) / C(N, n),
with N = 10, K = 4 (defective), n = 4.
a) All defective (k = 4):
P = C(4,4) C(6,0) / C(10,4) = 1 / 210 ≈ 0.00476.
b) None defective (k = 0):
P = C(4,0) C(6,4) / C(10,4) = 15 / 210 = 1/14 ≈ 0.07143.
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.