Conditional Probability

Question Description

I’m working on a question and need guidance to help me study.

The Dinghy Race. Alan is a member of dinghy sailing team. The Probability of strong winds tomorrow is 0.5. In strong winds, the probability of Alans team winning is 0.55. In light winds, the probability of Alans team winning falls to 0.3 Calculate the Probability that Alans team loses tomorrow P(Team Loses) = ? and Given that Alans team wins, find the Probability that the winds were strong. Probability = ?

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Final Answer

P (win) = .55(.5) + .25(.5)
= .275 + .125
= .40 or 40% Alan wins tomorrow

Given a win, P (wind_weak) = .125/.40
= .3125 or approximately 31.25%
This is called "posterior probability."

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