Lesson: Rewriting Questions

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Another possible solution to the question might be that the probability that the product is positive is equal to 1 - the probability that the product is negative, which is 1 - 12/42 or 2/7 and with the answer is 5/7. Where do I fail, because in the video you said that the answer is 3/7? This is the second time when using a different approach, which should be correct I receive different answer.
greenlight-admin's picture

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 the end all strategies and telling us when to use them. Your way of teaching is very effective.

Another way to solve the problem is to directly find the probability that the product of the first and second number selected are positive, as follows:
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
greenlight-admin's picture

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?
greenlight-admin's picture

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.
greenlight-admin's picture

I'm not sure about that solution.
Notice that 1 - 2/7 = 5/7 (not 3/7)

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