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25 Sep 2025, 06:39
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Minimum Survival: \(\frac{2}{5}\)
Maximum Survival: \(\frac{3}{5}\)
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
57% (00:58) correct
43%
(01:05)
wrong
based on 7
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History
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At a wildlife sanctuary, researchers track the survival of two newly released animal groups. Group A has a 3/5 chance of surviving its first winter, while Group B has a 4/5 chance of surviving its first winter.
Select for Minimum Survival the lowest probability, consistent with these estimates, that both groups survive the winter. Select for Maximum Survival the highest probability, consistent with these estimates, that both groups survive the winter. Make only two selections, one in each column.
Select for Minimum Survival the lowest probability, consistent with these estimates, that both groups survive the winter. Select for Maximum Survival the highest probability, consistent with these estimates, that both groups survive the winter. Make only two selections, one in each column.
| Minimum Survival | Maximum Survival | |
| \(0\) | ||
| \(\frac{1}{5}\) | ||
| \(\frac{2}{5}\) | ||
| \(\frac{1}{2}\) | ||
| \(\frac{3}{5}\) | ||
| \(\frac{4}{5}\) |
ShowHide Answer
Official Answer
Minimum Survival: \(\frac{2}{5}\)
Maximum Survival: \(\frac{3}{5}\)
25 Sep 2025, 06:39
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Official Solution:
• Minimum Survival Probability
We use the equation:
Total = P(A) + P(B) – P(both) + P(neither).
Substitute the values:
1 = 3/5 + 4/5 – P(both) + P(neither).
P(both) = 2/5 + P(neither).
To minimize P(both), we set P(neither) = 0.
This gives P(both) = 2/5.
Alternative we can do the following:
We are given:
P(A) = 3/5 (the probability that Group A survives),
P(B) = 4/5 (the probability that Group B survives).
This means the probability that Group B does not survive is:
P(not B) = 1 - P(B) = 1/5.
Now consider the event “A survives and B does not survive.” Its probability cannot be greater than either P(A) = 3/5 or P(not B) = 1/5. Therefore, the maximum possible probability of this event, “A survives and B does not survive,” is 1/5.
But P(A) = 3/5 represents all cases where A survives, and that breaks into two disjoint parts:
A survives and B survives, and
A survives and B does not survive.
So we can write:
P(A) = P(A and B) + P(A and not B).
We know P(A) = 3/5, and the maximum possible value of P(A and not B) is 1/5.
Therefore, the minimum possible value of P(A and B) is:
P(A and B) = 3/5 - 1/5 = 2/5.
So by this reasoning as well, the minimum survival probability for both is 2/5.
• Maximum Survival Probability
The probability of Group A surviving is 3/5 (60%) and the probability of Group B surviving is 4/5 (80%). The maximum probability that both survive cannot be greater than either one individually. Therefore, the maximum possible value of P(both) is the smaller of the two: 3/5 (60%).
Correct answer:
Minimum Survival "\(\frac{2}{5}\)"
Maximum Survival "\(\frac{3}{5}\)"
Bunuel
• Minimum Survival Probability
We use the equation:
Total = P(A) + P(B) – P(both) + P(neither).
Substitute the values:
1 = 3/5 + 4/5 – P(both) + P(neither).
P(both) = 2/5 + P(neither).
To minimize P(both), we set P(neither) = 0.
This gives P(both) = 2/5.
Alternative we can do the following:
We are given:
P(A) = 3/5 (the probability that Group A survives),
P(B) = 4/5 (the probability that Group B survives).
This means the probability that Group B does not survive is:
P(not B) = 1 - P(B) = 1/5.
Now consider the event “A survives and B does not survive.” Its probability cannot be greater than either P(A) = 3/5 or P(not B) = 1/5. Therefore, the maximum possible probability of this event, “A survives and B does not survive,” is 1/5.
But P(A) = 3/5 represents all cases where A survives, and that breaks into two disjoint parts:
A survives and B survives, and
A survives and B does not survive.
So we can write:
P(A) = P(A and B) + P(A and not B).
We know P(A) = 3/5, and the maximum possible value of P(A and not B) is 1/5.
Therefore, the minimum possible value of P(A and B) is:
P(A and B) = 3/5 - 1/5 = 2/5.
So by this reasoning as well, the minimum survival probability for both is 2/5.
• Maximum Survival Probability
The probability of Group A surviving is 3/5 (60%) and the probability of Group B surviving is 4/5 (80%). The maximum probability that both survive cannot be greater than either one individually. Therefore, the maximum possible value of P(both) is the smaller of the two: 3/5 (60%).
Correct answer:
Minimum Survival "\(\frac{2}{5}\)"
Maximum Survival "\(\frac{3}{5}\)"
