The probability that student passes a physics test is 2/3 and the probability that he passes both the physics and english test is 11/45. The probability that he passes at least one test is 4/5. The probability that he will passes english test will be ?

Question

Answer

Given:

Probability of passing physics test = 2/3

Probability of passing both physics and english test = 11/45

Probability of passing at least one test = 4/5

To find: Probability of passing english test

Solution:

Let A be the event of passing physics test and B be the event of passing english test.

Using conditional probability:

P(A and B) = P(A) * P(B|A)

We are given that P(A) = 2/3 and P(A and B) = 11/45.

Therefore,

P(B|A) = P(A and B) / P(A)
= (11/45) / (2/3)
= 11/30

Using probability of union of events:

P(A or B) = P(A) + P(B) - P(A and B)

We are given that P(A or B) = 4/5 and P(A) = 2/3.

Therefore,

P(B) = P(A or B) - P(A) + P(A and B)
= (4/5) - (2/3) + (11/45)
= 17/45

Final answer: Probability of passing english test is 17/45.

Explanation:

We can find the probability of passing english test in two ways - using conditional probability or using probability of union of events.

Using conditional probability, we first find the probability of passing both physics and english test given that the student has passed physics test. Then we use this probability along with the probability of passing physics test to find the probability of passing english test.

Using probability of union of events, we find the probability of passing english test by subtracting the probability of not passing both tests (i.e. the complement of passing at least one test) from the probability of passing at least one test.

Both methods give us the same answer of 17/45.

Answer

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