# Probability Worksheet

1If A and B are both random events.

Calculate:

1

2

3

4

5

6

7

2If A and B are both random events.

Calculate:

1

2

3

4

3Two balls are drawn from a box that contains one blue, one red, one green and one yellow ball. Define the sample space when:

1The first ball is returned to the box before drawing the second.

2The first ball is not returned to the box before the second is drawn.

4A box has 8 red balls, 5 yellow and 7 green. If a ball is extracted at random, calculate the probability that it will be:

1Red.

2Green.

3Yellow.

4Not red.

5Not yellow.

5A box contains three red balls and seven blue. Two balls are drawn at random. Define the sample space and find the probability of events when:

1The first ball is replaced before the second is drawn.

2The first ball is not replaced before the second is drawn.

6A ball is drawn from a box containing 4 red balls, 5 blue and 6 green. What is the probability that the ball will be red or white? What is the probability that it is blue?

7In a class there are 10 blonde girls, 20 brunette girls, 5 blonde boys and 10 brown-haired boys. If all 45 students attend class on a particular day, find the probability that a student selected at random will be:

1A boy.

2A brunette girl.

3A boy or girl.

8A die is rigged so that the probabilities of obtaining the different faces are proportional to the numbers on the faces (For example: A five is five times more likely to be rolled than a one). Find:

1The probability of obtaining a 6.

2The probability of obtaining an odd number.

9Two dice are thrown into the air simultaneously. Calculate:

1The probability that the sum of the dice will total 7.

2The probability that the sum of the dice will be an even number.

3The probability that the sum of the dice will be a multiple of three.

10Three die are thrown simultaneously. Calculate the probability of:

1Obtaining a six in all three die.

2 The sum of the dice equalling 7.

11When selecting a domino at random, calculate the probability of the domino being greater than 9 or a multiple of 4.

12Calculate the probability of obtaining the following outcomes when rolling a die:

1An even number.

2A multiple of three.

3A five or a six.

13Find the probability of obtaining the following outcomes when flipping two coins:

1Two heads.

2Two tails.

3One head and one tail.

14There are 20 raffle tickets in an envelope. Eight are for a car, and the rest are blank. Find the probability of drawing a ticket for the car if:

1Only one raffle ticket is extracted.

2Two raffle tickets are extracted.

3Three raffle tickets are extracted.

15Students A and B have probabilities of failing an exam of 1/2 and 1/5 respectively. The probability of them both failing the examination is 1/10. Determine the probability that at least one of the two students fail.

16Two brothers go hunting. The first brother kills an average of 2 animals every 5 shots and the second brother kills one animal every 2 shots. If the two fired at the same animal at the same time, what is the probability that they will obtain a kill?

17A class consists of 10 boys and 20 girls. Exactly half of the boys and half of the girls have brown eyes. Determine the probability that a randomly selected student will be a boy or a student with brown eyes.

18The probability that a husband and wife will still be living in 20 years is ¼ for the husband and is 1/3 for the wife. Calculate the probability:

1Of them both being alive in 20 years.

2The husband living in 20 years but not the wife.

3The husband and the wife dying before 20 years.