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?
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
=?
Post your answer for checking if you prefer to do so.
Note: In probabilities, it is preferable, whenever possible, to work in fractions (as opposed to decimals), which avoids ambiguities caused by round-off errors.
4/9
16/9
To find the probability that the student passes the test in mathematics, we can use the formula for the probability of the union of two events:
P(A or B) = P(A) + P(B) - P(A and B)
Let's assume event A represents passing the statistics test, and event B represents passing the mathematics test.
1. We are given that the probability of passing the statistics test (P(A)) is 2/3.
2. We are also given that the probability of passing both the statistics and mathematics tests (P(A and B)) is 14/45.
3. We know that the probability of passing at least one test is 4/5.
Using the formula, we can solve for P(B):
4/5 = 2/3 + P(B) - 14/45
First, we can simplify the equation:
4/5 = 30/45 + P(B) - 14/45
Next, we can combine like terms:
4/5 = (30 - 14 + 45P(B))/45
To isolate P(B), we'll multiply both sides of the equation by 45:
(45 * 4)/5 = 30 - 14 + 45P(B)
36 = 16 + 45P(B)
Subtracting 16 from both sides:
36 - 16 = 45P(B)
20 = 45P(B)
Finally, we can solve for P(B):
P(B) = 20/45
Therefore, the probability that the student passes the test in mathematics is 20/45, or approximately 0.444.