Question

First bag contains 7 blue marbles , 6 green marbles and another bag contains 2 blue marbles, 4 green marbles and 3 yellow marbles.

We draw a random marble from first bag and and place it to the other bag. Then We draw a marble from the second bag randomly and keep this one.

Calculate the probability that the marble we pick is green.

Answer 1

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Answer 2

ANSWER :

 P(green from first bag)

= Green marbles in the bag / Total marbles in the bag

= 6 / (7 + 6)

= 6/13

P(blue from first bag)

= blue marbles in the bag / Total marbles in the bag

= 7 / (7 + 6)

= 7/13

The marble chosen from the first bag is added to the second bag.

So,

P(green from second bag after addition of marble of first bag pick)

= P(green 1st bag) * P(green 2nd bag | 1st bag green) + P(blue 1st bag) * P(green 2nd bag | 1st bag blue)

= 6/13 * ((4 + 1) / (2 + (4 + 1) + 3)  + 7/13 * 4 / ((2 + 1) + 4 + 3)

= 6/13 * 5/10 + 7/13 * 4/10

= 58 / 130

= 0.4462 (ANSWER).