The probability that Ann passee statistics test is 5/7 and the probability that she passee economic test is 3/7.If the probability of passing at least one course is 6/7,what is the probability that she will pass both test?

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Answer 1 · 2016-02-20T20:36:34

Probability that Ann passes both tests is #2/7#

If we write that event #A# is "Ann passes probability test" and #B# is "Ann passes economic test" we can write the given data as:

#P(A)=5/7# probability of passsing statistics test

#P(B)=3/7# probability of passing probability test

#P(AuuB)=6/7# probability of passing at least one test

We are looking for probability that she passes both tests, so we are looking for #P(AnnB)#

According to the formula for probability of sum of two events we have:

#P(AuuB)=P(A)+P(B)-P(AnnB)#

If we transform it we can calculate that:

#P(AnnB)=P(A)+P(B)-P(AuuB)#, so:

#P(AnnB)=5/7+3/7-6/7=(5+3-6)/7=2/7#

So finally Probability that Ann passes both tests is #2/7#