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The probability of a fine day is 3/7 and the probability of a wet day is 4/7.

 

If it is a fine day:

The probability that a man cycles to work is 7/10.

The probability that a man drives to work is 2/10.

The probability that a man takes the train to work is 1/10.

 

If it is a wet day:

The probability that a man cycles to work is 1/9.

The probability that a man drives to work is 5/9.

The probability that a man takes the train to work is 3/9.

 

For a day selected at random, what is the probability that he takes the train to work?

 Feb 11, 2017
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Let P(E) denotes the probability of event E happening.

 

 P(takes train to work)

\(=\dfrac{3}{7}\times \dfrac{1}{10}+\dfrac{4}{7}\times \dfrac{3}{9}\\ =\dfrac{3}{70} + \dfrac{4}{21}\\ =\dfrac{7}{30}\)

 Feb 11, 2017

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