Question

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 the weather is cold and fred wins

what is the probability the weather is not cold and barney wins

Answer 1

Given

P( cold) = 0.75

P( Barney wins I cold ) = 0.30

P( Fred wins I not cold ) = 0.90

then , P( not cold ) = 1-0.75 =0.25

To find , P( cold and Fred wins) = ?

P(cold) = P(cold and  Fred wins ) + P( cold and Barney wins)

We know that , P( cold) = 0.75  

P(cold and  Barney wins ) = P( barney wins I cold ) *P( cold) =0.30 *0.75 = 0.225

Therefore ,  P(cold and  Fred wins ) = P(cold) - P( cold and Barney wins)  

= 0.75 -0.225

= 0.525

Probability that weather is cold and Fred wins =0.525

To find , P(not cold and Barney wins) = ?

P(not cold) = P(not cold and  Fred wins ) + P( not cold and Barney wins)

P(not cold) = 0.25

P(not cold and  Fred wins ) = P( Fred wins I not cold ) *P( not cold) = 0.90*0.25 = 0.225

thus ,

P( not cold and Barney wins) = P(not cold) - P(not cold and  Fred wins ) = 0.25 -0.225 = 0.025

Probability that weather is not cold and Barney wins =0.025