exercise:715d965436: Difference between revisions
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\newcommand{\mathds}{\mathbb}</math></div> (Chung<ref group="Notes" >K. L. Chung, ''Elementary | \newcommand{\mathds}{\mathbb}</math></div> (Chung<ref group="Notes" >K. L. Chung, ''Elementary Probability Theory With Stochastic Processes, 3rd ed.'' (New York: Springer-Verlag, 1979), p. 152.</ref>) | ||
Probability Theory With Stochastic Processes, 3rd ed.'' (New York: Springer-Verlag, 1979), p. 152.</ref>) | |||
In London, half of the days have some rain. The weather forecaster is correct 2/3 of the time, | 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 | 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 | does not rain, given that she has predicted that it won't rain, are both equal to 2/3. When rain is | ||
forecast, Mr. | forecast, Mr. Pickwick takes his umbrella. When rain is not forecast, he | ||
takes it with probability 1/3. Find | takes it with probability 1/3. Find | ||
<ul style="list-style-type:lower-alpha"><li> the probability that Pickwick has no umbrella, given that it rains. | <ul style="list-style-type:lower-alpha"><li> the probability that Pickwick has no umbrella, given that it rains. | ||
Latest revision as of 23:48, 12 June 2024
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(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 Pickwick has no umbrella, given that it rains.
- the probability that he brings his umbrella, given that it doesn't rain.
Notes