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15 Dec 2025, 09:00
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At least one: 0.9
p: 0.5
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:
70% (02:10) correct
30%
(02:18)
wrong
based on 344
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12 Days of Christmas Competition
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John has a 0.8 probability of eating breakfast with bacon and eggs, and Mary has a probability p of doing yoga in the morning.
If these events are independent, select for At least one the probability that at least one of these events occurs, and select for p the probability of Mary doing yoga in the morning that would be jointly consistent with the given information. Make only two selections, one in each column.
| At least one | p | |
| 0.2 | ||
| 0.4 | ||
| 0.5 | ||
| 0.85 | ||
| 0.9 | ||
| 0.95 |
ShowHide Answer
Official Answer
At least one: 0.9
p: 0.5
I31-16
15 Dec 2025, 10:00
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John has a 0.8 probability of eating breakfast with bacon and eggs, and Mary has a probability p of doing yoga in the morning.
If these events are independent, select for At least one the probability that at least one of these events occurs, and select for p the probability of Mary doing yoga in the morning that would be jointly consistent with the given information. Make only two selections, one in each column.
Since the events are independent, P(at least one) = P(breakfast) + P(yoga) - P(both). So, we get:
P(at least one) = P(breakfast) + P(yoga) - P(both) =
= 0.8 + p - P(breakfast) * P(yoga) =
= 0.8 + p - 0.8 * p =
= 0.8 + 0.2p
Obviously, P(at least one) must be greater than 0.8, so 0.85, 0.9, or 0.95.
Substituting 0.85 gives p = 0.25, which is absent from the options.
Substituting 0.9 gives p = 0.5, which is present in the options.
Therefore, the correct answer is p = 0.5, and the probability of at least one event occurring is 0.9.
GMAT-Club-Forum-yxtg1vxl.png [ 11.53 KiB | Viewed 2141 times ]
If these events are independent, select for At least one the probability that at least one of these events occurs, and select for p the probability of Mary doing yoga in the morning that would be jointly consistent with the given information. Make only two selections, one in each column.
Since the events are independent, P(at least one) = P(breakfast) + P(yoga) - P(both). So, we get:
P(at least one) = P(breakfast) + P(yoga) - P(both) =
= 0.8 + p - P(breakfast) * P(yoga) =
= 0.8 + p - 0.8 * p =
= 0.8 + 0.2p
Obviously, P(at least one) must be greater than 0.8, so 0.85, 0.9, or 0.95.
Substituting 0.85 gives p = 0.25, which is absent from the options.
Substituting 0.9 gives p = 0.5, which is present in the options.
Therefore, the correct answer is p = 0.5, and the probability of at least one event occurring is 0.9.
Attachment:
GMAT-Club-Forum-yxtg1vxl.png [ 11.53 KiB | Viewed 2141 times ]
General Discussion
15 Dec 2025, 09:40
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probabilty for atleast 1 of them happening is
1 - p(none of both)
1 - 0.2(1-p)
for p = 0.5 we get above as 0.9
hence answer is 0.9, 0.5
1 - p(none of both)
1 - 0.2(1-p)
for p = 0.5 we get above as 0.9
hence answer is 0.9, 0.5
