The probability that a regular scheduled flight departs on time is P(D)= 0.83; t
ID: 3341213 • Letter: T
Question
The probability that a regular scheduled flight departs on time is P(D)= 0.83; the probability that it arrives on time is P(A) = 0.82; and the probability that it departs on time and arrives on time is 0.78.
A. What is the probability that a plane arrives on time or departs on time?
B. What is the probability that a plane arrives on time givin that it departs on time?
C. What is the probability that a plane departs on time given that it arrives on time?
D. are these events (A,D) statistilly independent? Why?
E. If after two years P(A) = 0.9 and P(D) = 0.85 and P(A D) = 0.77; can we conclude that these events are mutually exclusive? Why? Are they Independent? why?
Explanation / Answer
P(A) = 0.82 P(D) = 0.83
P(A and D) = 0.78
A. P(A or D) = P(A) + P(B) - P(A and D)
= 0.82 + 0.83 - 0.78
= 0.87.
B. P(A|D) = P(A and D) / P(D)
= 0.78 / 0.83
= 0.9398.
C. P(D|A) = P(A and D) / P(A)
= 0.78 / 0.82
= 0.9512.
D. Since P(A) and P(A|D) are different, the events are not statistically independent.
E. (Note: This question is not stated correctly. What does P(A D) mean?)
Since P(A and D) is not zero, the events are not mutually exclusive.
P(A|D) = 0.77 / 0.85 = 0.9059.
Since P(A) and P(A|D) are different, the events are not independent.
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