BlueSky Air has the best on-time arrival rate with 80% of its flights arriving on time. A test is conducted by randomly selecting 16 BlueSky Air flights and observing whether they arrive on time.
What is the probability that 2 flights of BlueSky Air arrive late? (Please carry answers to at least six decimal places in intermediate steps. Give your final answer to the nearest three decimal places).
Answer is (0.8^14 * 0.2^2 * (16 * 15))/2
Should I use the binomial theorem for this question?
2014-08-11 10:17 pm
回答 (1)
2014-08-11 10:27 pm
Yes.
Binomial probability:
P(X = k) = C(n, k) * p^k * q^(n-k)
In your case you want to figure the probability that exactly 14 are on-time (which will be 2 that are late).
n : total trials (16)
k : successes (14)
p : probability of success as a decimal (0.80)
q : probability of failure (1 - p = 0.20)
C(16,14) * 0.8^14 * 0.2^2
P.S.
C(16, 14) = 16 x 15 / (2 x 1)
Binomial probability:
P(X = k) = C(n, k) * p^k * q^(n-k)
In your case you want to figure the probability that exactly 14 are on-time (which will be 2 that are late).
n : total trials (16)
k : successes (14)
p : probability of success as a decimal (0.80)
q : probability of failure (1 - p = 0.20)
C(16,14) * 0.8^14 * 0.2^2
P.S.
C(16, 14) = 16 x 15 / (2 x 1)
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