A bag contains 6 black and 3 white balls Another bag contains 5 black and 4 white balls If one ball is drawn from each bag find the probability that these two balls are of the same color?

Answer 1

14/27 ~ 0.519 ~ 51.9%

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EXPLANATION

For bag 1: Probability of drawing a black ball; P(B1) =

6/9. A white one; P(W1) =3/9

For bag 2: P(B2) =

5/9. P(W2) =

4/9.

Probability of drawing a black ball from each bag: P(B1UB2) =

(6/9)∙(5/9) =

10/27

Probability of drawing a white ball from each bag: P(W1UW2) =

(3/9)∙(4/9) =

4/27

The probability of drawing 2 balls of the same color is the sum of the above

probabilities:

P(2 same color balls) =

P(B1UB2) + P(W1UW2) =

10/27 +4/27 =

14/27 =

0.5185...

P(2 same color balls) ~ 0.519 ~ 51.9%