the probability that a student pass a test in statistics is 2/3, and the probability that both a test in statistics and mathematics is 14/45. the probability that passes at least one test is 4/5. what is the probability that passes the test in mathematics?

Answer 1

S=event of passing statistics
M=event of passing mathematics
P(S)=2/3
P(M∪S)=4/5
P(M∩S)=14/45
From the given information, we can apply the following relation, which is always valid, mutually exclusive or not.

P(M∪S)=P(M)+P(S)-P(M∩S)
in other words,
P(M)=P(M∪S)-P(S)+P(M∩S)
=4/5-2/3+14/45
=?

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Note: In probabilities, it is preferable, whenever possible, to work in fractions (as opposed to decimals), which avoids ambiguities caused by round-off errors.

Answer 2

4/9

Answer 3

16/9