About 24% of flights departing from New York\'s John F. Kennedy International Ai

Question

About 24% of flights departing from New York's John F. Kennedy International Airport were delayed in 2009. Assuming that the chance of a flight being delayed has stayed constant at 24%, we are interested in finding the probability of 10 out of the next 100 departing flights being delayed. Noting that if one flight is delayed, the next flight is more likely to be delayed, which of the following statements is correct? . (A) We can use the geometric distribution with n = 100, k = 10, and p = 0.24 to calculate this probability. (B) We can use the binomial distribution with n = 10, k = 100, and p = 0.24 to calculate this probability. (C) We cannot calculate this probability using the binomial distribution since whether or not one flight is delayed is not independent of another. (D) We can use the binomial distribution with n = 100, k = 10, and p = 0.24 to calculate this probability

Explanation / Answer

Correct Answer : (C) We cannot calculate this probability using the binomial distribution since whether or not one flight is delayed is not independent of another.

Explanation :

We want to find probability of a fixed number of successes in a given number of trials of an experiment. Therefore, Geometric distribution is not the correct one to use. Geometric distribution is used to find probability of having "k" no. of trials until 1st success is observed. Hence (A) is wrong.

Key assumption underlying the binomial distribution is that in the full collection of trials, each trial is independent of the other trials i.e. occurence of a particular outcome on a particular trial doesn't change our beliefs about the outcome of any other trial. However, in this question, it is clearly mentioned that "if one flight is delayed, the next flight is more likely to be delayed". Hence, the key assumption of Binomial distribution is violated. So (B) and (D) are wrong and (C) is correct.

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