Math Probabilities (P2)

1.  The Cool Gents is a R&B group planning their next concert tour. The band has a total of 25 new songs in their repertoire.

a.  How many different set lists of 12 songs can the group select to play on tour? Use permutations or combinations. (Hint: the order of the songs is not relevant.)

b.  How many different ways are there for the group to record a CD consisting of 12 songs chosen from 25 new songs?  Use permutations or combinations. (Hint: The order in which the songs appear on the CD is relevant).

2.  A card is drawn out of a standard deck of 52 cards. Each card can be described by giving its "value" (A, 2,3,4,….10, J, Q, K) and its "suit" (H for hearts, C for clubs, D for diamonds and S for spades). For example, 2S denotes the two of spades and KH denotes the king of hearts. Write out the event described by each of the following statements as a set.

a.  E₁: "draw a king."

b.  E₂: "draw a club."

c.  E₃:  "draw a face card."  (A "face" card is a jack, queen or king).

3.  A card is drawn at random out of a well-shuffled deck of 52 cards. Find the probability of each of the following events. (Do problem #2 first.)

a.  E₁: "draw a king."

b.  E₂: "draw a club."

c.  E₃: "draw a face card."  (A "face" card is a jack, queen, or king).

4.  An honest coin is tossed three times in a row. Find the probability of each of the following events.

a.  E₁: "the coin comes up heads exactly twice."

b.  E₂: "all three tosses come up the same."

c.  E₃: "exactly half of the tosses come up heads."

d.  E₄: "the first two tosses come up tails."