Question

One of two boxes contains 4 red balls and 2 green balls and the second box contains 4 green and two red balls. By design, the probabilities of selecting box 1 or box 2 at random are 1 3 for box 1 and 2 3 for box 2. A box is selected at random and a ball is selected at random from it. (a) Given that the ball selected is red, what is the probability it was selected from the first box? (b) Given that the ball selected is red, what is the probability it was selected from the second box?

Answer 1

Step-by-step explanation:

Probability that the ball drawn is red and from ! =P(R/A)

P(R/A)=

P(B/R)×P(B)+P(A/R)×P(A)

P(A/R)×P(A)

P(R/A)=

5

3

,P(R/B)=

9

5

P(A)=

2

1

,P(B)=

2

1

P(R/A)=

9

5

×

2

1

+

5

3

×

2

1

5

3

×

2

1

=

104

54

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