exercise:2e924de49d: Difference between revisions
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(Created page with "(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 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. Pickw...") |
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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. 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. | 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. | ||
<ul class="mw-excansopts"> | |||
<li>0</li> | |||
<li>1/3</li> | |||
<li>1/2</li> | |||
<li>2/3</li> | |||
<li>7/9</li> | |||
</ul> | |||
'''Notes''' | '''Notes''' | ||
{{Reflist|group=Notes}} | {{Reflist|group=Notes}} | ||
'''References''' | |||
{{cite web |url=https://math.dartmouth.edu/~prob/prob/prob.pdf |title=Grinstead and Snell’s Introduction to Probability |last=Doyle |first=Peter G.|date=2006 |access-date=June 6, 2024}} | |||
Latest revision as of 01:48, 23 June 2024
(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
References
Doyle, Peter G. (2006). "Grinstead and Snell's Introduction to Probability" (PDF). Retrieved June 6, 2024.