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The odds against an event is 5 : 3 and the odds in favour of another independent event is 7 : 5. Find the probability that at least one of the two events will occur.
- a)52/96
- b)69/96
- c)71/96
- d)13/96
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
The odds against an event is 5 : 3 and the odds in favour of another i...
P (E1) 3/8
P (E2) = 7/12.
Event definition is: E1 occurs and E2 does not occur or E1 occurs and E2 occurs or E2 occurs and E1 does not occur.
Event definition is: E1 occurs and E2 does not occur or E1 occurs and E2 occurs or E2 occurs and E1 does not occur.
(3/8) x (5/12) + (3/8) x (7/12) + (5/8) x (7/12) = 71/96.
Most Upvoted Answer
The odds against an event is 5 : 3 and the odds in favour of another i...
To find the probability that at least one of the two events will occur, we can consider the complementary probability, which is the probability that neither of the events occur.
Let's first find the probability of the first event not occurring. The odds against the first event are given as 5 : 3, which means that the probability of the first event not occurring is 5/(5+3) = 5/8.
Similarly, the probability of the second event not occurring is 7/(7+5) = 7/12, as the odds in favor of the second event are given as 7 : 5.
Since the two events are independent, the probability that neither of the events occur is the product of their individual probabilities: (5/8) * (7/12) = 35/96.
Now, let's find the probability that at least one of the events occur. This is equal to 1 minus the probability that neither of the events occur:
P(at least one event occurs) = 1 - P(neither event occurs) = 1 - 35/96 = 61/96.
Therefore, the correct answer is option 'C': 61/96.
Let's first find the probability of the first event not occurring. The odds against the first event are given as 5 : 3, which means that the probability of the first event not occurring is 5/(5+3) = 5/8.
Similarly, the probability of the second event not occurring is 7/(7+5) = 7/12, as the odds in favor of the second event are given as 7 : 5.
Since the two events are independent, the probability that neither of the events occur is the product of their individual probabilities: (5/8) * (7/12) = 35/96.
Now, let's find the probability that at least one of the events occur. This is equal to 1 minus the probability that neither of the events occur:
P(at least one event occurs) = 1 - P(neither event occurs) = 1 - 35/96 = 61/96.
Therefore, the correct answer is option 'C': 61/96.
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The odds against an event is 5 : 3 and the odds in favour of another independent event is 7 : 5. Find the probability that at least one of the two events will occur.a)52/96b)69/96c)71/96d)13/96Correct answer is option 'C'. Can you explain this answer?
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