# Worksheet: Compound Events

In this worksheet, we will practice finding and interpreting the probability of compound events.

**Q6: **

A fair six-sided die with the numbers 1 to 6 is rolled, and a fair coin is flipped. What is the probability that the number obtained on the die is a factor of 12 and the coin lands with its heads side down?

- A
- B
- C
- D
- E

**Q7: **

and are independent events, where and . What is the probability that events and both occur?

- A
- B
- C
- D
- E

**Q8: **

In an experiment a coin is flipped and a die is rolled once. Event is the appearance of a head and a prime number. Event is the appearance of an even number. Find the probability of event or event occurring but not both.

- A
- B
- C
- D

**Q10: **

A coin is flipped three consecutive times. What is the probability of only getting one head?

- A
- B
- C
- D

**Q11: **

A fair coin is flipped and a fair die is rolled. What is the probability of rolling an even number on the die?

- A
- B
- C
- D

**Q12: **

An experiment consists of flipping a coin and rolling a fair six sided die once. Determine the probability of event , the coin landing head side up and the dice landing with a prime number uppermost.

- A
- B
- C
- D
- E

**Q13: **

A card is drawn at random from a deck of cards numbered from 1 to 25. What is the probability that the card drawn has a number which is a factor of 10 or is even?

- A
- B1
- C0
- D
- E

**Q14: **

A bag contains 4 white marbles, 2 black marbles, and 5 red marbles. If a marble is selected at random, find the probability of selecting a black or a red marble.

- A
- B
- C
- D
- E

**Q16: **

A bag contains 6 blue balls and 15 red balls. If two balls are drawn without replacement, what is the probability of getting one blue ball and one red ball?

- A
- B
- C
- D

**Q17: **

A deck contains eight cards which are numbered 5, 7, 8, 9, 9, 15, 19, and 20. What is the probability of selecting a card at random which has a prime number?

- A
- B
- C
- D

**Q18: **

If these two spinners are spun, what is the probability that the sum of the numbers the arrows land on is a multiple of 5?

- A
- B
- C
- D
- E

**Q19: **

A bag contains colored balls, 18 of which are red. The rest of the balls are black. Two red balls are removed from the bag, and then a ball is drawn at random. What is the probability that the ball drawn is black, given that there were 99 balls in the bag at the start?

- A
- B
- C
- D

**Q20: **

For two events and , when is it true that ?

- Awhen the events are dependent
- Bwhen the events are disjoint
- Cwhen one of the events is a subset of the other
- Dwhen the events are intersected
- Ewhen the events are independent

**Q21: **

A bag contains 32 balls. There are 27 red balls numbered from 1 to 27 and 5 white balls numbered from 28 to 32. If a ball is chosen at random from the bag, what is the probability that the ball is white or has an odd number?

- A
- B
- C
- D
- E

**Q22: **

A bag contains 19 balls, 5 of which are white, 6 are red, and 8 are black. If a ball is drawn at random, what is the probability of the ball being black or white?

- A
- B
- C
- D
- E

**Q23: **

The table shows the number of tyres, from a sample of 800, which needed to be replaced after a range of distances. Using the table, calculate the probability that a tyre will need to be replaced after covering more than 50 kilometres.

Distance (km) | D 50 | 50 D 100 | 100 D 150 | D 150 |
---|---|---|---|---|

Number of Damaged Tyres | 140 | 230 | 200 | 230 |

- A
- B
- C
- D

**Q24: **

In a sample of 55 people, 28 of them have brown hair and 22 of them have blue eyes. 5 of them have neither brown hair nor blue eyes. What is the probability that a random person from the sample has at least one of these features.

- A
- B
- C
- D
- E

**Q25: **

A bag contains 5 red balls, 9 yellow balls, and 6 black balls. What is the probability that a ball selected at random is red or black?

- A
- B
- C
- D
- E