You have 2 biased coins. Coin A comes up heads with probability 1/4, while coin B comes up heads with probability 3/4. However, you don’t know which is which, so you choose a coin randomly and flip it. If the flip is heads, you guess the flipped coin is B, otherwise you guess it is coin A. What is the probability that your guess is correct?

Alice tosses a fair coin and throws a 6-sided die. Then, Bob tosses a fair coin and throws a 6-sided die too. If the sides they got for the coin flips are the same, Alice wins. If the sides they got for the coin flips are different, then whoever got the bigger number for their die roll wins. Otherwise, it's a tie.  What is the probability of a tie?

There are 9 women and 8men with a chance to be on a game show. The producer of the show is going to choose 10 of these people at random to be contestants. What is the probability that the producer chooses 4 women and 6 men?  Is this using the C and P and doing it on the calculator?

A gunball machine contains 5 red gumballs, 3 blue gumballs, and 4 yellow gumballs. You put a coin in the machine, and two gumballs come out one after the other. What is the probability that the first gumball that comes out is blue and the second gumboil is red?