A basket contains 20 apples and 10 oranges out of which 5 apples and 3 oranges are defective. If a person takes out 2 at random, then the probability that either both are apples or both are good is 316435.
A
True
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B
False
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Solution
The correct option is A True
Out of 30 items, two can be selected in 30C2 ways.
So total number of elementary event 30C2
Consider the following events:
A= Getting two apples;
B= Getting two good items
Required probability
=P(A∪B)=P(A)+P(B)−P(A∩B)....(i)
There are 20 apples, out of which 2 can be drawn in 30C2 ways.
∴P(A)=20C230C2
There are 8 defective pieces and the remaining 22 are good. Out of 22 good pieces, two can be selected in 22C2 ways
∴P(B)=22C230C2
Since there are 15 pieces which are good apples out of which 2 can be selected in 15C2 ways. Therefore, P(A∩B)= Probability of getting 2 pieces which are good apples