1. One ball is drawn at random from a bag containing 4 red balls and 6 white balls. What is the probability that the ball is a) red? b) white? c) white or red? d) white and red?

2. If you draw one card at random from a deck of 12 cards numbered 1 through 12, inclusive. What is the probability that the number you draw is divisible by 4?
3. A die is rolled. What is the probability that

a) a 4 will result? b) a 7 will result? c) an odd number will result?

4. An urn contains three red balls numbered 1, 2, 3, four white balls numbered 4, 5, 6, 7, and three black balls numbered 8, 9, 10. A ball is drawn from the urn. What is the probability that the ball is
a) red? b) odd-numbered? c) white and odd-numbered?

d) red or odd-number? e) red or even-number? f ) black or white?

5. From a deck of 52 ordinary playing cards, one card is drawn. Find the probability that it is
a) a queen b) a red card c) a red king

d) a spade e) a king or a black card f ) an odd-numbered black card

6. Suppose a fair coin is tossed four times. Construct an equiprobable sample space for the experiment, and determine each of the following probabilities:

a) P (2 heads) b) P (3 heads) c) P (4 heads)

7. A distinguishable pair of fair dice is rolled. Find

a) P (sum is 4) b) P (sum is 10) c) P (sum is 12)

8. A ball is drawn from a bag containing 13 red balls numbered 1-13 and 5 white balls numbered 14-18. What is the probability that
a) the ball is not red? b) the ball is not even-numbered
c) the ball is red and even-numbered? d) the ball is white or odd-numbered?
e) the ball is neither red nor even-numbered?

Ventspils Augstskola - Jesu´s A. C´azares 2

9. A distinguishable pair of fair dice is rolled. What sum is most likely to occur?
10. If the odds that a particular horse will win a race are 1:20. What is the probability (a) that the horse will win the race? (b) that the horse will lose the race?
11. A car rental firm has 425 cars. Sixty-three of these cars have defective turn signals and 32 have defective tires. What is the probability that one of these cars selected at random (a) has defective turn signals? (b) has defective tires?
12. In a sales promotion, a clothing store gives its customers a chance to draw a ticket from a box that contains a discount on their next purchase. The box contains 3000 tickets giving a 10% discount, 500 giving a 30% discount, 100 giving a 50% discount, and 1 giving a 100% discount. What is the probability that a given customer will randomly draw a ticket giving

a) a 100% discount? b) a 50% discount? c) a discount of less than 50%?

13. A dry cleaning firm has 12 employees: 7 women and 5 men. Three of the women and five of the men are 40 years old or older. The remainder are over 20 years of age and under 40. If a person is chosen at random from this firm, what is the probability that the person is

a) a woman? b) under 40 years of age? c) 20 years old?

14. Of 100 students, 24 can speak French, 18 can speak German, and 8 can speak both French and German. If a student is picked at random, what is the probability that he or she can speak French or German?
15. At the Baker Engineering Company, 40% of the employees are female and 60% of the em- ployees earn less than AC 40, 000. If 30% of the employees are females who earn less than AC 40, 000. What is the probability that an employee picked at random is female or earns less than AC 40, 000?