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Updated on: 17 Sep 2024, 11:28
Originally posted by vsgamtttttt on 06 Dec 2023, 00:33.
Last edited by Bunuel on 17 Sep 2024, 11:28, edited 6 times in total.
Last edited by Bunuel on 17 Sep 2024, 11:28, edited 6 times in total.
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Least Probability for Both: 10%
Greatest Probability for Both: 50%
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
60% (01:42) correct
40%
(02:24)
wrong
based on 1443
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According to a prominent investment adviser, Company X has a 50% chance of posting a profit in the coming year, whereas Company Y has 60% chance of posting a profit in the coming year.
Select for Least probability for both the least probability, compatible with the probabilities provided by the investment adviser, that both Company X and Company Y will post a profit in the coming year. And select for Greatest probability for both the greatest probability, compatible with the probabilities provided by the investment adviser, that both Company X and Company Y will post a profit in the coming year. Make only two selections, one in each column.
Select for Least probability for both the least probability, compatible with the probabilities provided by the investment adviser, that both Company X and Company Y will post a profit in the coming year. And select for Greatest probability for both the greatest probability, compatible with the probabilities provided by the investment adviser, that both Company X and Company Y will post a profit in the coming year. Make only two selections, one in each column.
ID: 700202
| Least Probability for Both | Greatest Probability for Both | |
| 5% | ||
| 10% | ||
| 25% | ||
| 50% | ||
| 60% | ||
| 80% |
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Least Probability for Both: 10%
Greatest Probability for Both: 50%
04 Jan 2024, 23:07
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According to a prominent investment adviser, Company X has a 50% chance of posting a profit in the coming year, whereas Company Y has 60% chance of posting a profit in the coming year.
Select for Least probability for both the least probability, compatible with the probabilities provided by the investment adviser, that both Company X and Company Y will post a profit in the coming year. And select for Greatest probability for both the greatest probability, compatible with the probabilities provided by the investment adviser, that both Company X and Company Y will post a profit in the coming year. Make only two selections, one in each column.
An intuitive way to handle this question is to see the following.
The maximum probability of any event occurring is 1. So, the maximum probability that either X will post a profit or Y will post a profit is 1.
Now, since 50% + 60% > 1, we see that there must be some times when both occur. In other words, the occurrences of the two events must overlap some of the time. After all, if they didn't overlap, the probability that one or the other would occur would be greater than 1.
If you think about it, the minimum overlap must be 10%. After all, if we fill up 50% of the possible total probability of 1 with the probability that X will be profitable, then we have only 50% of the possible total probability of 1 left for Y. However, the probability that Y will be profitable is 60%. So, that 60% - 50% = 10% extra must overlap with the occurrence of X being profitable.
In mathematical terms, P(X or Y) = P(X) + P(Y) - P(X and Y), and it must be the case that P(X or Y) ≤ 1.
So, if P(X) + P(Y) = 0.5 + 0.6 = 1.1, then to reduce 1.1 to the maximum P(X or Y) of 1, we need to subtract at least 0.1.
Thus, P(X and Y) must be at least 0.1, meaning the correct answer for Least Probability for Both is 10%.
Then, the maximum probability that both will occur at the same time must be 50% since the maximum probability of X posting a profit is 50% and the probability of both posting a profit can't be greater than the probability that one of them will.
So, the correct answer for Greatest Probability for Both is 50%.
Correct Answer: 10%, 50%
Select for Least probability for both the least probability, compatible with the probabilities provided by the investment adviser, that both Company X and Company Y will post a profit in the coming year. And select for Greatest probability for both the greatest probability, compatible with the probabilities provided by the investment adviser, that both Company X and Company Y will post a profit in the coming year. Make only two selections, one in each column.
An intuitive way to handle this question is to see the following.
The maximum probability of any event occurring is 1. So, the maximum probability that either X will post a profit or Y will post a profit is 1.
Now, since 50% + 60% > 1, we see that there must be some times when both occur. In other words, the occurrences of the two events must overlap some of the time. After all, if they didn't overlap, the probability that one or the other would occur would be greater than 1.
If you think about it, the minimum overlap must be 10%. After all, if we fill up 50% of the possible total probability of 1 with the probability that X will be profitable, then we have only 50% of the possible total probability of 1 left for Y. However, the probability that Y will be profitable is 60%. So, that 60% - 50% = 10% extra must overlap with the occurrence of X being profitable.
In mathematical terms, P(X or Y) = P(X) + P(Y) - P(X and Y), and it must be the case that P(X or Y) ≤ 1.
So, if P(X) + P(Y) = 0.5 + 0.6 = 1.1, then to reduce 1.1 to the maximum P(X or Y) of 1, we need to subtract at least 0.1.
Thus, P(X and Y) must be at least 0.1, meaning the correct answer for Least Probability for Both is 10%.
Then, the maximum probability that both will occur at the same time must be 50% since the maximum probability of X posting a profit is 50% and the probability of both posting a profit can't be greater than the probability that one of them will.
So, the correct answer for Greatest Probability for Both is 50%.
Correct Answer: 10%, 50%
