Question

please help!

A researcher wants to conduct a genetic study using 10 randomly-selected volunteers. He has a volunteer pool of 20, composed of 10 males and 10 females. What is the probability that the randomly-selected group will be all male OR all female?
A. 1/184,756
B. 1/92,378
C. 5/138,567
D. 1/138,567

Answer 1

@whpalmer4

Answer 2

Let's say you want all males.

For the first selection, the probability of choosing a male is 10/20. After 1 male is removed from the pool, the probability of choosing a male on the second selection is 9/19. Then 8/18, 7/17...1/11 for the final candidate. Multiply all of those fractions together.

Now that first selection could really be regarded as starting two parallel computations going. If you choose a male, the computation goes as above. However, if you choose a female, the computation also goes as above, except this time you're trying to pick females. Therefore, the final answer is 2*the probability computed in the paragraph above, because you successfully choose a study group either way.