A basket contains 5 apples and 7 oranges and another basket contains 4 apples and 8 oranges. One fruit is picked out from each basket. The probability that the fruits are both apples or both oranges, is

Options

A. `24//144`
B. `56//144`
C. `68//144`
D. `76//144`

Answer

D

Explanation

P(selecting an apple from both baskets)
=P(apple from first basket).
P(Apple from second basket)
`=(""^(5)C_(1))/(""^(12)C_(1)).(""^(4)C_(1))/(""^(12)C_(1))`
P(selecting an orange from both baskets)
=P(Orange from first basket).
P(Orange from second basket)
`=(""^(7)C_(1))/(""^(12)C_(1)).(""^(8)C_(1))/(""^(12)C_(1))`
`:.` Required probability
`=(""^(5)C_(1).""^(4)C_(1))/(""^(12)C_(1).""^(12)C_(1))+(""^(7)C_(1).""^(8)C_(1))/(""^(12)C_(1).""^(12)C_(1))`
`=(20+56)/(144)=(76)/(144)`