1.In the card game, "Between the Sheets," each player is dealt two cards, face up. Ace is low and king is high. The player can then fold or bet that the value of a third dealt card will be between the values of the two original cards. The bet is lost if the third card is above, below, or matches the first two cards. You have been dealt two cards. What is the probability of winning the bet if your cards are dealt:

a)a three and a nine?

b)a four and a ten?

c)a five and a Queen?

d)an ace and a king?

e)a pair of jacks?

2.Explain the mistake in the following statements.

a.The probability that a mineral sample will contain silver is 0.38, and the probability that it will not contain silver is 0.52.

b.The probability that a drilling operation will be a success is 0.34, and the probability that it will not be a success is -0.066.

c.The probability that a student will get an A in a geology course is 0.32, and the probability that he or she will get either an A or B is 0.27.

3.What is the probability of the following events?

a.An odd number appears on the single toss of a fair die.

b.A black card is drawn when drawing a single card from an ordinary deck of 52 cards

c.A black card or red card is drawn when drawing a single card from an ordinary deck of 52 cards

d.Do not get a heart when drawing a single card from an ordinary deck of 52 cards

e.An ace, a ten of diamonds, or a three of clubs appears in drawing a single card from an ordinary deck of 52 cards.

4.The probability that an integrated circuit chip will have a defective etching is 0.12, the probability that it will have a crack defect is 0.29, and the probability that it will have both defects is 0.07.

a.What is the probability that a chip will have either an etching or a crack defect?

b.What is the probability that a chip will have neitherdefect?

5.A car rental agency has 18 compact cars and 12 intermediate -size cars. If four of the cars are randomly selected for a safety check, what is the probability of getting two of each kind?

6.An experiment consists of drawing one card from a deck of 52 cards. What is the probability that the card is:

a.the ace of spades

b.ared jack

c.a three of clubs or a six of diamonds

d.any suit but clubs

e.a ten or a king?

f.the card is a spade or an ace

g.neither a four or a club?

7.What is the probability of making a 7 in one throw of a pair of dice?Find the probability of the other sums.

8.From an ordinary deck of playing cards, cards are drawn successively at random and without replacement. Compute the probability that the third spade appears on the sixth draw.

9.A coin is tossed 3 times, and 2 heads and 1 tail fall. What is the probability that the first toss was heads?

10.A hand of five cards is to be dealt at random and without replacement from an ordinary deck of 52 playing cards. Find the conditional probability of an all spade hand given that there are 4 spades in the hand.

11.A coin is tossed 3 times. Find the probability that all 3 are heads if

a. it is known that the first two are heads,

b. if it is known that 2 of them are heads.

12.A committee is composed of six Democrats and five Republicans. Three of the Democrats are men, and three of the Republicans are men. If a man is chosen for chair, what is the probability that he is a Republican?

13.Two chips are drawn without replacement from an urn containing five black chips and three green chips. What is the probability that a) the second chip drawn is green if the first one was green, and b) the second chip drawn is black if the first one was black?