The probability that a student passes Mathematics is 2/3 and the probability that he passes English is 4/9. If the probability that he will pass at least one subject is 4/5, then what is the probability that he will pass (i) Both the subjects? (ii) Exactly one of the subjects? (iii) At most one of the subjects? (iv) Non of the subjects?
The probability that a student passes Mathematics is 2/3 and the probability that he passes English is 4/9. If the probability that he will pass at least one subject is 4/5, then what is the probability that he will pass (i) Both the subjects?
The probability of a students passing jssc a maths exam is 70% what is the probability that the student will fail
14/45
The probability that a student passes Mathematics is 2/3 and the probability that he passes English is 4/9. If the probability that he will pass at least one subject is 4/5, then what is the probability that he will pass (i) Both the subjects? (ii) Exactly one of the subjects...
To solve this problem, we can use basic probability rules and formulas. Let's break down each part of the question.
(i) Probability of passing both subjects:
To find the probability of passing both Mathematics and English, we multiply the probabilities of passing each subject together. Therefore, the probability of passing both subjects is (2/3) * (4/9) = 8/27.
(ii) Probability of passing exactly one subject:
To find the probability of passing exactly one subject, we need to consider the cases of passing Mathematics only and passing English only. The probability of passing Mathematics only is (2/3) * (5/9) = 10/27, and the probability of passing English only is (1/3) * (4/9) = 4/27. Therefore, the probability of passing exactly one subject is (10/27) + (4/27) = 14/27.
(iii) Probability of passing at most one subject:
The probability of passing at most one subject includes the cases of passing exactly one subject and passing no subjects. We have already calculated the probability of passing exactly one subject as 14/27. To find the probability of passing no subjects, we subtract the probability of passing at least one subject from 1. Since the probability of passing at least one subject is given as 4/5, the probability of passing no subjects is 1 - (4/5) = 1/5. Therefore, the probability of passing at most one subject is (14/27) + (1/5) = 65/135 or 13/27.
(iv) Probability of passing none of the subjects:
The probability of passing none of the subjects is the complement of passing at least one subject. Since the probability of passing at least one subject is given as 4/5, the probability of passing none of the subjects is 1 - (4/5) = 1/5.
In summary:
(i) Probability of passing both subjects: 8/27
(ii) Probability of passing exactly one subject: 14/27
(iii) Probability of passing at most one subject: 13/27
(iv) Probability of passing none of the subjects: 1/5