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13 Jan 2026, 11:37
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At least one: 0.9
\(p\): 0.5
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.
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 |
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Official Answer
At least one: 0.9
\(p\): 0.5
13 Jan 2026, 11:37
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Official Solution:
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.
Correct answer:
At least one "0.9"
\(p\) "0.5"
Bunuel
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.
Correct answer:
At least one "0.9"
\(p\) "0.5"
