exercise:2e924de49d

Jun 21'24

Exercise

(Chung^{[Notes 1]}) In London, half of the days have some rain. The weather forecaster is correct 2/3 of the time, i.e., the probability that it rains, given that she has predicted rain, and the probability that it does not rain, given that she has predicted that it won't rain, are both equal to 2/3. When rain is forecast, Mr. Pickwick takes his umbrella. When rain is not forecast, he takes it with probability 1/3. Find the probability that he brings his umbrella, given that it doesn't rain.

0
1/3
1/2
2/3
7/9

Notes

K. L. Chung, Elementary Probability Theory With Stochastic Processes, 3rd ed. (New York: Springer-Verlag, 1979), p. 152.

References

Doyle, Peter G. (2006). "Grinstead and Snell's Introduction to Probability" (PDF). Retrieved June 6, 2024.

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Jun 23'24

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[1] K. L. Chung, Elementary Probability Theory With Stochastic Processes, 3rd ed. (New York: Springer-Verlag, 1979), p. 152.

[Notes 1]