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Assume that each bag contains 6 balls. Bag a contains 3 red and 3 white, while bag b contains 2 red, 2 white, and 2 blue. You randomly select one ball from bag a, note the color, and place the ball in bag b. You then select a ball from bag b at random and make note of its color.(1) What is the probability that both balls are red? (2) What is the probability that both balls are red given that the first ball you drew was red?

Question

Assume that each bag contains 6 balls. Bag a contains 3 red and 3 white, while bag b contains 2 red, 2 white, and 2 blue. You randomly select one ball from bag a, note the color, and place the ball in bag b. You then select a ball from bag b at random and make note of its color.

(1) What is the probability that both balls are red? 



(2) What is the probability that both balls are red given that the first ball you drew was red?

check_circleAnswer
Step 1

Given that each bag contains 6 balls, Bag A contains 3 red and 3 white while Bag B contains 2 red and 2 white and 2 blue.

Step 2

1) Obtain the probability that both the balls are red as,

3
P(first ball selected from bag A is red)
6
3
P( first ball selected from bag B is red)
6
3 3
P(both balls are red)
6 6
4
X
help_outline

Image Transcriptionclose

3 P(first ball selected from bag A is red) 6 3 P( first ball selected from bag B is red) 6 3 3 P(both balls are red) 6 6 4 X

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Step 3

2) Obtain the probability that both the balls a...

3
P(B R A R)=
6
1
2
help_outline

Image Transcriptionclose

3 P(B R A R)= 6 1 2

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