Question

Toy wooden blocks are packaged in bags of 9. One bag contains 6 maple blocks and 3 birch blocks, while a second bag contains 5 maple blocks and 4 birch blocks. One block is drawn from the first bag and placed into the second one. What is the probability that a block now drawn at random from the second bag will be a maple?

Answer #1

Concerning the block drawn from the first bag :

P(maple) = ⅔ (case 1)

P(birch) = ⅓ (case 2)

In case 1, the second bag contains 6 maple and 4 birch, therefore
probability of drawing maple = 6/10.

In case 2, the second bag contains 5 maple and 5 birch, therefore
probability of drawing maple = 5/10.

Since the probability of case 1 = ⅔,

and the probability of case 2 = ⅓ ,

the total probability of drawing maple from the second bag
=

(⅔)(6/10) + (⅓) (5/10)

= 12/30 + 5/30

= 17/30

= 0.5667

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