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The odds in favour of one student passing a test are 3:7.The odds against another student passing at are 3:5.The probability that both pass is
- a)7/16
- b)21/80
- c)9/80
- d)3/16
Correct answer is option 'D'. Can you explain this answer?
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The odds in favour of one student passing a test are 3:7.The odds agai...
Solution:
Given that odds in favor of one student passing a test is 3:7 and the odds against another student passing the test is 3:5.
Let A be the event that the first student passes the test and B be the event that the second student passes the test.
Calculating the Probability of A and B:
We can calculate the probability of A and B using the following formulas:
- Probability of A = Odds in favor of A / (Odds in favor of A + Odds against A)
- Probability of B = Odds against B / (Odds in favor of B + Odds against B)
Substituting the given values, we get:
- Probability of A = 3 / (3 + 7) = 3/10
- Probability of B = 3 / (3 + 5) = 3/8
Calculating the Probability of both A and B:
We can calculate the probability of both A and B using the multiplication rule of probability:
- Probability of A and B = Probability of A x Probability of B
Substituting the calculated values, we get:
- Probability of A and B = (3/10) x (3/8) = 9/80
Therefore, the probability that both students pass the test is 9/80.
Hence, Option (D) 3/16 is incorrect and the correct option is (C) 9/80.
Given that odds in favor of one student passing a test is 3:7 and the odds against another student passing the test is 3:5.
Let A be the event that the first student passes the test and B be the event that the second student passes the test.
Calculating the Probability of A and B:
We can calculate the probability of A and B using the following formulas:
- Probability of A = Odds in favor of A / (Odds in favor of A + Odds against A)
- Probability of B = Odds against B / (Odds in favor of B + Odds against B)
Substituting the given values, we get:
- Probability of A = 3 / (3 + 7) = 3/10
- Probability of B = 3 / (3 + 5) = 3/8
Calculating the Probability of both A and B:
We can calculate the probability of both A and B using the multiplication rule of probability:
- Probability of A and B = Probability of A x Probability of B
Substituting the calculated values, we get:
- Probability of A and B = (3/10) x (3/8) = 9/80
Therefore, the probability that both students pass the test is 9/80.
Hence, Option (D) 3/16 is incorrect and the correct option is (C) 9/80.
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The odds in favour of one student passing a test are 3:7.The odds against another student passing at are 3:5.The probability that both pass isa)7/16b)21/80c)9/80d)3/16Correct answer is option 'D'. Can you explain this answer?
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