SOLUTION: During the cold season,the sun is visible 25% of the time .The probability that the class of mathematicians enjoys a lesson is 70% when the sun is visible and only enjoys a lesson

Question 1044547: During the cold season,the sun is visible 25% of the time .The probability that the class of mathematicians enjoys a lesson is 70% when the sun is visible and only enjoys a lesson 30% when it is cloudy.What is the probability that the mathematicians will enjoy a lesson on a given cold day?
Found 2 solutions by robertb, chewe :
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
P(enjoys) = P(sun visible)*P(enjoys|sun visible) + P(sun not visible)*P(enjoys|sun not visible) = 0.25*0.70 + 0.75*0.30 = 0.40.
Answer by chewe (1) (Show Source): You can put this solution on YOUR website!

p(enjoying )= p(sun visible )*p(enjoying the lesson )/p( sun visible ) + p(sun not visible )*p(enjoying when is cloudy ) /p(when not visible )
0.25*0.7/0.25 + 0.75*0.30/0.75= 1 hence the p( enjoying ) = 1.
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