A hat contains 22 names, 10 of which are female. If five names are randomly drawn from the hat, what is the probability that at least four female names are drawn?

Question

anonymous · Answer

420

anonymous · Answer

YA KONT

anonymous · Answer

The answer is actually 0.105 YA DUNCE

anonymous · Answer

Now, can someone actually help me solve this step by step

anonymous · Answer

10 females
12 males
5 will be randomly be chosen.
Restriction: at least 4 females should be chosen (it can be 4 F or 5 F)
This is equals to only 1 OR none males.
So it will be: 
(10 C 4 x 12C 1) + (10 C 5 x 12C 0)

Without restriction, there are 22 people and 5 will be chosen, so 22C5

Probability of having at least 4 females will be:
$\sf \Large \frac{( _{10} C_4 \times  _{12}C_1) + ( _{10} C_ 5 \times  _{12}C_0)}{ _{22}C_5}$

anonymous · Answer

Thank you so  much! I have been waiting for someone to help me with this problem for a while and havent gotten much of a response. Now thanks to you I understand this problem easily :)