Question

A population consists of 25 men and 25 women. A simple random sample (draws at random without replacement) of 4 people is chosen. Find the chance that in the sample the third person is a woman, given that the first person and fourth person are both men. Pls give calculations.

Answer 1

The possible arrangements of the first three people selected are:
M W W
M W M
M M M
M M W
Two of these arrangements have a woman selected third:
1) where women are the second and the third selections.
2) where a man is selected second and a woman third.

The probability of selecting women on the second and third selections is
\[P(women\ second\ +\ third)=\frac{25C2}{49C2}\]
The probability of selecting a woman on either the second or third selection is
\[P(1\ woman\ on\ either\ second\ or\ third\ selection)=\frac{25\times 24}{49C2}...........(1)\]
But a woman on the third selection is required, therefore the probability found in (1) must be halved to give
\[P(man\ on\ second\ selection, woman\ on\ third)=\frac{25\times 24}{49C2}\times \frac{1}{2}........(2)\]
The probability that in the sample of 3 people the third person is a woman is
\[\frac{25C2}{49C2}+(\frac{25\times 24}{49C2}\times \frac{1}{2})\]

Answer 2

thnk you... i got that!

Answer 3

You're welcome :)