Question
Asked Oct 1, 2019

Assume that the box contains 10 balls: 5 red, 2 green, and 3 blue. Two balls are drawn at random, one after the other without replacement.

What is the probability that the first ball was blue, given that the second was red?

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Expert Answer

Step 1

The probability that first was blue and given that second was red is,

Subscripts 1 and 2 represent first draw and second draw.

P(B/R)P(BR)
P(R.)
P(B,)x P(R.)
P(R.)
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P(B/R)P(BR) P(R.) P(B,)x P(R.) P(R.)

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Step 2

Now, the value of P(R2) is,

...
P(R)-(P(B)x P(R)) + (P(R)x P(R)) + (P (G)x P(R.))
5
5
4
2
5
X
X
10 9
10 9
10 9
1
2
1
_
6
9 9
1
2
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P(R)-(P(B)x P(R)) + (P(R)x P(R)) + (P (G)x P(R.)) 5 5 4 2 5 X X 10 9 10 9 10 9 1 2 1 _ 6 9 9 1 2

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Advanced Math