The probability that a student passes a physics test is 2/3 and the probability that he passed both physics test and an english test is 14/15. The probability. The probability that he passes at least one test is 4/5. What is the probability that he passes the english test.
To find the probability that a student passes the English test, we need to understand the relationships between the events.
Let's define the events:
A = The event that the student passes the physics test.
B = The event that the student passes the English test.
We are given the following information:
P(A) = 2/3 (probability of passing the physics test)
P(A∩B) = 14/15 (probability of passing both physics and English test)
P(A∪B) = 4/5 (probability of passing at least one test)
To find P(B), we can apply the concept of probability using set theory:
P(A∪B) = P(A) + P(B) - P(A∩B)
Substituting the given information:
4/5 = 2/3 + P(B) - 14/15
We can now solve for P(B):
4/5 - 2/3 + 14/15 = P(B)
(12/15 - 10/15 + 14/15) = P(B)
16/15 = P(B)
However, probabilities can never be greater than 1, so P(B) must be less than or equal to 1.
Therefore, the probability that the student passes the English test is 16/15, which is not a valid probability.