Question

In: Statistics and Probability

the probability that the weather will be cold on sunday is .75 if the weather is...

the probability that the weather will be cold on sunday is .75 if the weather is cold there is a probability of 0.30 that barney wins if the weather is not cold there is a probablity of 0.90 that fred will win

what is the probability

barney wins the match

fred wins the match

Solutions

Expert Solution

P[ the weather will be cold on Sunday ] = 0.75

P[ the weather will not be cold on Sunday ] = 1 - P[ the weather will be cold on Sunday ] = 1 - 0.75 = 0.25

P[ Barney wins | the weather will be cold on Sunday ] = 0.3

P[ Fred wins | the weather will be cold on Sunday ] = 1 - P[ Barney wins | the weather will be cold on Sunday ] = 1 - 0.3 = 0.7

P[ Fred will win | the weather will not be cold on Sunday ] = 0.9

P[ Barney will win | the weather will not be cold on Sunday ] = 1 - P[ Fred will win | the weather will not be cold on Sunday ] = 1 - 0.9 = 0.1

P[ Barney wins and the weather will be cold on Sunday ] = P[ Barney wins | the weather will be cold on Sunday ]*P[ the weather will be cold on Sunday ]

P[ Barney wins and the weather will be cold on Sunday ] = 0.3*0.75

P[ Barney wins and the weather will be cold on Sunday ] = 0.225

P[ Barney will win and the weather will not be cold on Sunday ] = P[ Barney will win | the weather will not be cold on Sunday ]*P[ the weather will not be cold on Sunday ]

P[ Barney will win and the weather will not be cold on Sunday ] = 0.1*0.25

P[ Barney will win and the weather will not be cold on Sunday ] = 0.025

P[ Barney wins ] = P[ Barney wins and the weather will be cold on Sunday ] + P[ Barney will win and the weather will not be cold on Sunday ]

P[ Barney wins ] = 0.225 + 0.025

P[ Barney wins ] = 0.250

P[ Barney wins ] = 0.25

P[ Fred wins ] = 1 - P[ Barney wins ]

P[ Fred wins ] = 1 - 0.25

P[ Fred wins ] = 0.75

orchestra answered 1 year ago
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