Independent flips of a coin that lands on heads with probability p are made. What is the probability that the first four outcomes are:
(a) H, H, H, H
(b) T, H, H,H
(c) What is the probability that the pattern T, H, H, H occurs before the pattern
H, H, H, H? JUSTIFY YOUR ANSWER BY DEFINING EVENTS.

Six people will decide which of them are on a committee by flipping a coin. Each person flips the coin, and is on the committee if he or she gets a head. What is the probability that someone is on the committee, but not all six people?

A hat contains n coins, f of which are fair and b of which are biased to land on heads with a probability of 2/3. A coin is drawn from the hat and tossed twice. The first time it lands heads and the second time it lands tails.
Given this information, what is the probability that a fair coin has been chosen?

Al, Bob and Carlos are playing a silly game. Al flips a coin. If he gets heads, the game ends and he wins. If not, Bob flips the coin. If he gets heads, the game ends and he wins. If not, Carlos flips the coin. If he gets heads, the game ends and he wins. If not, the coin is returned to Al and the process begins again.

Six students will decide which of them are on a committee by flipping a coin. Each student flips the coin, and is on the committee if he or she gets a head. What is the probability that someone is on the committee, but not all 6 students?

Six students will decide which of them are on a committee by flipping a coin. Each student flips the coin and is on the committee if he or she gets a head. What is the probability that someone is on the committee, but not all 6 students?

52) (from pg. 52) A coin, having probabiliyt p of landing heads, is flipped until head apears for the rth time. Let N denote the number of flips required.
a) Calculate E[X] for the maximum random variable fo Exercise 37.
b) Calculate E[X] for X as in Exercise 33.
c) Calculate E[X] for X as in Exercise 34.

1. A coin is flipped 50 times.
a)Calculate the probability that exactly 10 coinflips are heads.
b)Calculate the probability that 10 coinflips or less are heads.
2.The expected number of work accidents in a year is 11.5.
a) Calculate the probability that there are exactly 10 accidents in a randomly selected year.

A group of n people meet at lunch for a cup of coffee. They play a game to see who gets to pay for all the coffees. Each person flips a coin. If all the coins come up the same except for one person, then that one person gets to pay for all the coffee. If the coins do not result in this way, then everyone flips again until there