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Question

A bag contains 3 red and 7 black balls. Two balls are drawn one by one at a time at random without replacement. If second drawn ball is red then what is the probability the first drawn ball is also red?

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Solution

Number of red balls =3
Number of black balls =7
Total number of balls =10
Let ,P(A)= Probability that first is red
P(B)= Probability that second is red
If second is red, there are 2 possible ways
Either first is red and second is red.
Or first is black and second is red.
So,
P(B)=3C110×2C19+7C110×3C19
=690+2190
=2790
=310
Probability that first is red, given second is red
P(A/B)=P(AB)P(B)
=3C110×2C19310
=690310
=690×103
=627
=29

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