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## Comment on

Rewriting Questions## Another possible solution to

## P(product is negative) = P

P(product is negative) = P(1st # is neg and 2nd # is pos OR 1st # is pos and 2nd # is neg)

= P(1st # is neg and 2nd # is pos) + P(1st # is pos and 2nd # is neg)

= (4/7 x 3/6) + (3/7)(4/6)

= 12/42 + 12/42

= 24/42

= 4/7

So, P(product is positive) = 1 - 4/7

= 3/7

## Thank you for summarizing at

## Another way to solve the

P(prod pos) = P(#1 neg and #2 neg) + P(#1 pos and #2 pos)

P(#1 neg and #2 neg) = P(#1 neg) * P(#2 pos | #1 neg)

= 4/7(3/6) = 12/42

P(#1 pos and #2 pos) = P(#1 pos) * P(#2 pos | #1 pos)

= 3/7 * (2/7) = 6/42

P(prod pos) = 12/42 + 6/42 = 18/42 = 3/7

## Perfect!!!!

Perfect!!!!

## Hello Brent,

I always have this doubt in probability- It is a confusion between Mutually exclusive events and Independent events. Though I understand both these concepts individually, but I get bit confused when it comes to questions. Like here in this question explained in module, how did you tell that the events of selecting 1 boy and 2 boys are mutually exclusive? Please explain. Also will mutually exclusive events be independent events as well? Please clarify. Pls explain the other method of solving also, that is the first method of : P(atleast 1 boy) = P(1 boy) + P(2 boys). How to calculate P(2 boys) here? I have doubt. Will it be 2/8? which is 1/4?

## QUESTION: How did you tell

QUESTION: How did you tell that the events of selecting 1 boy and 2 boys are mutually exclusive?

If events A and B are mutually exclusive, then P(A AND B) = 0.

In this question, the probability of selecting exactly 1 boy AND selecting exactly 2 boys is ZERO. That is, if you select 2 people, it cannot be the case that those two people consist of 1 boy AND consist of 2 boys.

QUESTION: Will mutually exclusive events be independent events as well?

If events A and B are possible (that is P(A) > 0 and P(B) > 0), then the two events cannot be both independent and mutually exclusive.

QUESTION: Pls explain the other method of solving also, that is the first method of : P(at least 1 boy) = P(1 boy) + P(2 boys). How to calculate P(2 boys) here?

We have a few ways to calculate both parts. Here's one option.

P(1 boy) = P(1st person is boy and 2nd person is girl OR 1st person is girl and 2nd person is boy)

= [P(1st person is boy) x P(2nd person is girl)] + [P(1st person is girl) x P(2nd person is boy)]

= [4/8 x 4/7] + [4/8 x 4/7]

= 2/7 + 2/7

= 4/7

P(2 boys) = P(1st person is boy AND 2nd person is boy)

= P(1st person is boy) x P(2nd person is boy)

= 4/8 x 3/7

= 3/14

So, P(at least 1 boy) = P(1 boy) + P(2 boys)

= 4/7 + 3/14

= 11/14

## Thanks a ton Brent!

## Hi Brent,

I did it this way:

the counter probability = p(one number is positive) * P(one number is negetive) = (4/7) * (1/2) = 2/7

Hence, the probability is 1 - 2/7 = 3/7.

## I'm not sure about that

I'm not sure about that solution.

Notice that 1 - 2/7 = 5/7 (not 3/7)

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