exercise:715d965436: Difference between revisions
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(Created page with "<div class="d-none"><math> \newcommand{\NA}{{\rm NA}} \newcommand{\mat}[1]{{\bf#1}} \newcommand{\exref}[1]{\ref{##1}} \newcommand{\secstoprocess}{\all} \newcommand{\NA}{{\rm NA}} \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>) In London, half of the days have some rain. The weather forecaster is correct 2/3 of th...") |
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forecast, Mr.\ Pickwick takes his umbrella. When rain is not forecast, he | 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><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. | ||
</li> | </li> | ||
<li> the probability that he brings his umbrella, given that it doesn't rain. | <li> the probability that he brings his umbrella, given that it doesn't rain. | ||
Revision as of 00:48, 13 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