Statistics Problem

Question

A group of foreign students formed a club. In total there were 12 Germans, 8 French, 6 Spanish and 6 Italian.

A team of 5 students was going to be randomly selected to participate in a University function.

What is the probability that among those 5, there are 2 German students?

What is the probability that among those 5, there are greater than or equal to 2 German students?

Answer 1

I will answer the 1st question. Whenever you pick from select groups you can count all the possible ways you can select the event you are looking for divided by the total possible events:

(₁₂C₂)(₂₀C₃)/(₃₂C₅) Picking 2 G out of 12 * Picking 3 NonG out of 20 / Picking 5 out of 32 (Combinations)

Another way is to count the probabilities without replacement and account for not considering order

(12/32 * 11/31 *20/30*19/29*18/28) That's the probability of GG NG NG NG in that order.

Now multiply be ₅C₂ which is all the different orders that the 2 G can be picked out of 5

These yield the same probability of about 40%

In the second problems solve for 0 G and 1 G probabilities and subtract from 1.