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A bag contains 5 apples and 7 oranges an...

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

A

`(24)/(144)`

B

`(56)/(144)`

C

`(68)/(144)`

D

`(76)/(144)`

Text Solution

Verified by Experts

The correct Answer is:
C
Consider the following events:
`A_(i)`=Getting an apple from `i^(th)` basket
`O_(i)`= Getting an orange from `i^(th)` basket
Required probability
`=P((A_(1) cap O_(2)) cup (O_(1) cap A_(2)))`
`=P(A_(1) cap O_(2))+P(O_(1) cap A_(2))`
`=P(A_(1))P(O_(2)) + P(O_(1))P(A_(2))=(5)/(12)xx(8)/(12)+(7)/(12)xx(4)/(12)=(68)/(144)`
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