Probability of drawing two married couples

[turutk]

Homework Statement

Names of 8 people (4 married couples) are written down to equally sized papers. Two carbilds are drawn. What is the probability of drawing a married couple? (it is not specified if the cards were drawn at the same time or one-by-one)

Homework Equations

na

The Attempt at a Solution

So the probability of drawing a woman is 4/8 the probability of drawing her husband is 1/7 when multiplied the result is 1/14 but the correct answer is 1/7. (non combination solution would be better)

 

[tiny-tim]

hi turutk!

So the probability of drawing a woman is 4/8 …

why does it have to be a woman?

 

[turutk]

i thought it wouldn't matter but now i think that i need to multiply 1/12 by 2.

also i got the solution. 4 married couples could be drawn. a total of 8C2 can be drawn. 4/8C2 = 1/7


thanks for your answer

 

[HallsofIvy]

Yes, it does matter. Actually, you question is a little ambiguous. Do you put all 8 names in the same container so you might draw two men or two women, or do you draw men and women separately? Drawing "one by one" or "both at the same time" does NOT matter.

Assuming all 8 are put into a single container, you draw one name. Now, there are seven names left and exactly one of those is the first person's spouse. What is the probability of that spouse being drawn?

If all four men are put into one container and all four women in another, it's slightly different. You draw a person from one container (whether it is a man or a woman doesn't matter). Now there are four people left in the other container and one of them is the first person's spouse. What is the probability now?

 

[turutk]

names of 8 people are put into a box and 2 cards are drawn. so it can be woman-woman, woman-man, man-woman, man-man