Question: FOUR DECIMAL ANSWERS. You are charged with the responsibility to determine the probability of coincidental birthdays. Initially the following two birthday questions were assigned to you.

a. Ignoring leap years, find the probability that two randomly chosen people were born on January 1.

b. Ignoring leap years, find the probability that two randomly selected people have the same birthday.

c. You have a bag containing 1 red ball, 2 blue balls, 3 yellow balls, 4 black balls and 5 white balls. What is the probability of drawing without replacement a red ball, then a blue ball and lastly a yellow ball in the first three draws?

d. For problem 3c how many different combinations are possible for the draw?

e. For problem 3c how many different permutations are possible for the draw?

f. A statistics professor tosses three coins that cannot be seen by any student. One student asks if at least one of the coins turned up heads and another student asks the same question for tails. Given that the professor’s response to both questions is “yes”, find the probability that two of coins turned up heads?