Question

A researcher wants to conduct a genetic study using 25 randomly-selected volunteers. He has a volunteer pool of 30, composed of 15 males and 15 females. What is the probability of 12 male and 13 female volunteers OR 13 male and 12 female volunteers being selected at random for the study?
A. 17/522
B. 455/522
C. 105/522
D. 175/261

Answer 1

do you know about combinations?

Answer 2

no

Answer 3

@xGuardians

Answer 4

@iambatman

Answer 5

15C12 * 15C13 + 15C13 * 15C12
________________ ________________
30C 25 30 C 25

Answer 6

This problem is sampling without replacement.
\[P(12\ males)=\frac{15C12\times15C13}{30C25}=\frac{\frac{15!}{12!3!}\times\frac{15!}{13!2!}}{\frac{30!}{25!5!}}\]
The probability of 13 males is the same as for 12 males, therefore the required probability is found by doubling the result for 12 males.

Answer 7

@ajaylounsber

Answer 8

yeh?

Answer 9

can't help this time sorry bro

Answer 10

The calculation for the probability of 12 male and 13 female volunteers OR 13 male and 12 female volunteers being selected at random for the study is:
\[2\times\frac{15\times14\times13\times15\times14\times5\times4\times3\times2}{3\times2\times2\times30\times29\times28\times27\times26}=you\ can\ calculate\]