Serious Answers oNly Please!!! HElpp me with this one pleasee?

Question

box a contains 8 items of which 3 are defective, and box B contains 5 items of which 2 are defective. An item is drawn at random from each box. 1) what is the probability that both items are non-defective? 2) What is the probability that one item is defective and one not? 3) If one item is defective and one is not, what is the probability that the defective item came from box A?

Answer 1

5 out of the 8 items in Box A are non-defective.
3 out of the 5 items in Box B are non-defective.

The probability that an item from Box A and an item from Box B are drawn and are both non-defective is:

5/8 * 3/5 = 3/8

The probability that an item from Box A and an item drawn from Box B and both defective is:

3/8 * 2/5 = 3/20.

This means that the probability that one of the two items drawn is defective is:

1 - p(both are not defective) - p(both are defective)
=1 - 3/8 - 3/20
= 19/40

We can see this by showing all possible outcomes. The items in Box A are shown on the top edge, and the items in Box B are shown on the right edge

N N N N N D D D
A A A A A B B B N
A A A A A B B B N
A A A A A B B B N
B B B B B C C C D
B B B B B C C C D

The events marked "A" represent 2 non-defective items. The events marked "B" represent 1 defective and 1 non-defective item. The events marked "C" represent 2 defective items.

Out of 19 events where there is 1 defective and 1 non-defective item, the defective item came from box A 9 times.

So if 1 item is defective and 1 is not, the probability is 9/19 that it came from box A

Answer 2

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