PERMUTATION AND COMBINATIONS

please help with the formulas for these problems!

1.  During the last hour, a telemarketer dialed 25 numbers and reached 7 busy signals, 3 answering machines, and 15 people. Use this information to determine the empirical probability that the next call will be answered in person.

1.  If you roll a die many times, what would you expect to be the relative frequency of rolling a number less than 5?

A) 2 out of 3        B)  1 out of 3    C) 1 out of 6      D) 1 out of 2               E) 5 out of 6

1.  A jar contains 4 yellow marbles, 12 green marbles, and 11 black marbles. If one marble is selected at random, what is the probability that it is not yellow?

1.  One card is selected at random from a standard 52-card deck of playing cards. Find the probability that the card selected is a jack.

1.  The odds against Thunderbolt winning the Birmingham Derby are 11:3. Find the probability that Thunderbolt wins.

A)  3/11             B) 3/14              C) 8/11              D) 8/14             E) 3/8

1.  500 tickets for prizes are sold for $2 each. Five prizes will be awarded – one for $300, one for $200, and three for $50. Steven purchases one of the tickets.

a) Find the expected value

b) Find the fair price of the ticket.

1.  Two balls are to be selected without replacement from a bag containing one red, one blue, one green, and one yellow ball. How many points are there in the sample space?