Please help-Probability

[dddanny2006]

John invites 12 Friends to a dinner party,half of which are men.Exactly one man and one woman are bringing deserts.If one person from this group is selected at random ,what is the probability that it is a woman who is not bringing deserts or a man who is not bringing deserts

6 men 6 women

(5/6)dont bring deserts (5/6) dont bring deserts

Probability is (5/6)+(5/6)

I know that Im wrong.Please tell me the conceptual mistake that Im making.


Thank you

Dan

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Hi dddanny2006,

This question tells us that there are 12 total people (6 men and 6 women). If we're going to randomly select one person from this group, then the solution will have to be "out of 12."

We're asked for the probability of picking someone who DID NOT bring a desert (either male or female is acceptable).

We have 10 people who didn't bring a desert, so the probability is 10/12 = 5/6

GMAT assassins aren't born, they're made,
Rich

[sanju09]

John invites 12 Friends to a dinner party,half of which are men.Exactly one man and one woman are bringing deserts.If one person from this group is selected at random ,what is the probability that it is a woman who is not bringing deserts or a man who is not bringing deserts

6 men 6 women

(5/6)dont bring deserts (5/6) dont bring deserts

Probability is (5/6)+(5/6)

I know that Im wrong.Please tell me the conceptual mistake that Im making.


Thank you

Dan

You will select one from the total, which is 12, not 6. And there are 10 such people in the group as required. Rest is well.

It's a nice idea to write down your own approach over the wrong answered questions. It helps us repair it only where it's needed. It seems that you might miss this little concept that probability of any event can never exceed 1, otherwise you should on your own be surprised to find probability (5/6) + (5/6)!

[Mathsbuddy]

Or with more detailed processing:

M = P(MAN) = 1/2
W = P(WOMAN) = 1/2

D = P(any individual bringing a dessert) = 1/6
D' = P(...not bringing a dessert) = 5/6

P([W and D'] or [M and D']) = [1/2 * 5/6] + [1/2 * 5/6] = 5/6

I prefer Rich's method because its quicker. Thankfully my answer concurs!