Question 1110066: This quarter, there is a 50% chance that Jason will pass accounting, a 60% chance the he will pass english, and 80% chance that he will pass at least one of these two courses. What is the probability that he will pass both accounting and english?
Found 3 solutions by stanbon, ikleyn, greenestamps:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! This quarter, there is a 50% chance that Jason will pass accounting, a 60% chance the he will pass english, and 80% chance that he will pass at least one of these two courses. What is the probability that he will pass both accounting and english?
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P(pass account and eng) = 0.5*0.6 = 0.3
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Cheers,
Stan H.
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Answer by ikleyn(52784)  (Show Source):
You can put this solution on YOUR website! .
Use the general formula of the Probability theory
P(Accounting OR English)) = P(Acc) + P(Eng) - P(Acc AND English).
With the given data, this equation / (equality) takes the form
80% = 50% + 60% - P(Acc AND Eng) ====> (it implies that)
P(Acc AND Eng) = 50% + 60% - 80% = 30%.
Answer. The probability that he will pass both Accounting and English is 30%, under the given conditions.
Answer by greenestamps(13200)  (Show Source):
You can put this solution on YOUR website!
The problem is over-constrained; however, the constraints are consistent with one another.
To calculate the probability that he passes both classes, you only need to multiply the probabilities of his passing each class: 0.5*0.6 = 0.3.
With those numbers, the given information that there is an 80% chance of passing at least one of the courses is extraneous.
P(pass both) = 0.3
P(pass accounting only) = 0.5-0.3 = 0.2
P(pass english only) = 0.6-0.3 = 0.3
It follows (without having to be specified in the problem) that
P(pass at least one) = 0.3+0.2+0.3 = 0.8.
So the more complicated calculation shown by the other tutor, while valid, is more work than is required.
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