csaluja wrote:

Princ wrote:

Bunuel wrote:

A certain gym has 900 male members and 1200 female members. Three hundred of the male members are married to women who have memberships at the gym. If one man and then one woman are selected at random, what is the probability that they are a married couple?

A. 0

B. 1/14693

C. 1/3600

D. 1/1050

E. 1

OA:CProbability of Selecting Male (Married couple)\(= \frac{300}{900}\)

Probability of Selecting female Married to male selected earlier\(= \frac{1}{1200}\)

Final probability\(= \frac{300}{900} * \frac{1}{1200} = \frac{1}{3600}\)

Hello,

I was wondering could you please explain how you got 1/1200? 300 men married to 300 women. Shouldn't the probability of selecting a woman is 300/1200? Would greatly appreciate it if you could please help eliminate my doubt!

csalujaProbability of Selecting Male (Married couple)\(= \frac{300}{900}\)....(1)

We have to select 1 married male out of total 900 males, so we have 300 options.Probability of Selecting female Married to male selected earlier\(= \frac{1}{1200}\)

There are 300 married women amongst total 1200 female, but as we have to find the probability of a married couple being selected, Number of favorable case for selecting a female who is married to male already selected in (1) is 1. Total number of selecting one female (without any constraint) is 1200.

Another Method of solving There are total \(300\) couples.

Favorable case: Selecting \(1\) couples of \(300\) couples : \(300C1 = \frac{300!}{299!*1!} = 300\)

Total number of cases : Selecting \(1\) male out of \(900\) males and Selecting \(1\) female out of \(1200\) females

\(= 900C1 * 1200C1 = \frac{900!}{899!*1!}*\frac{1200!}{1199!*1!}=900*1200\)

Probability of selecting a married couple :\(\frac{Favorable \quad cases}{Total \quad number \quad of \quad cases}= \frac{300}{900*1200} = \frac{1}{3600}\)

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