Question

suppose that we draw cards repeatedly and with replacement from a file of 200 cards ,100 of which refer to male and 100 which refer to female persons.what is the probability of obtaining the second "female" card before the third "male" card?

Answer 1

Step-by-step explanation:

So we "win" if 2 females occur before the third male. We could enumerate cases, but here is another way.

We modify the game slightly, by drawing 4 cards whatever happens. Then we will have at least 2 females or at least 3 males, and we cannot have both. Also, we win the first game precisely if in the modified game we have 2 or more females. By standard techniques, the probability of this is

(42)124+(43)124+(44)124.