Given that, P(rain in the afternoon ) = 0.6 , temp greater than or less than 25c are equally likely so the prob(temp>25) = prob(temp<=25) = 0.5 , P(rain in the afternoon ∣ temp<=25) = 0.4 .
We need to find out the value of P(rain in the afternoon ∣ temp> 25) .
Apply conditional property
P(rain in the afternoon ) =P(rain in the afternoon ⋂ temp<= 25) +
P(rain in the afternoon ⋂ temp>25)
0.6 = P(temp<=25).P(rain in the afternoon ∣ temp<= 25) +
P(temp>25).P(rain in the afternoon ∣ temp> 25)
0.6 = 0.5⨉0.4 + 0.5 ⨉ P(rain in the afternoon ∣ temp> 25)
P(rain in the afternoon ∣ temp> 25) = 0.8
The correct answer is (C) 0.8