97) If the average of 3a and 4b is less than 50 and a is twice b, what
1 answer:
The average of and
satisfies
Then
, so if
must be an integer, then the largest integer value it can take on is 19 if
can be a rational number (in which case
) or 18 if
must also be an integer.
Given that none of the provided answer choices lists 18 or 19, I'd bet there's a typo and you're supposed to find the maximum integer value of , in which case the answer would be B as the largest integer value would be 9.
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Answer:
Explanation:
This is a typical problem of conditional probability.
In this case you know:
- the probability of the event D <em>(an international flight leaving the U.S. is delayed in departing</em>), which is 0.36 and you can write as P(D) = 0.36
- the probability of event P <em>(an international flight leaving the U.S. is a transpacific flight</em>), which is 0.25 and you can write as P(P) = 0.25;
- the joint probability of event P and D (<em>international flight leaving the U.S. is a transpacific and is delayed in departing</em>), which is 0.09 and you can write as P (P ∩ D) = 0.09.
You need to determine the <em>probability that an international flight leaving the United States is delayed given that the flight is a transpacific flight</em>, i.e. the conditional probability P (D/P).
Hence, use the formula for conditional probability:
- P (D/P) = P (D ∩ P) / P(D) = P (P ∩ D) / P (D)
- P (D/P) = 0.09 / 0.25 = 0.36