3 boxes contains 10 fruits each.If the number of mangoes in the 3 boxes is 4,5,6 respectively.find the probability that a fruit picked at random from one of the boxes is mango? with Explaination

Solve using bayes theorem
P=1/3 into4/10+1/3 into5/10+1/3into6/10 where 1/3 is the probability of choosing the 1 box from 3box and 4/10 is the probability of pick the fruit is a mango from the 1st box

P = P(first box is selected)*P(mango is selected from the first box) + P(second box is selected)*P(mango is selected from the second box) + P(third box is selected)*P(mango is selected from the third box)

= 1/3 * 4/10 + 1/3 * 5/10 + 1/3 * 6/10
= 15/30 = 1/2