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?
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
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