Q1. Tina has two bags of counters. Bag A has 5 red and 3 blue counters. Bag B has 4 red and 5 blue counters. Tina takes one counter from each bag at random.

Background

Topic: Probability Trees and Compound Probability

This question tests your understanding of probability trees and how to calculate probabilities for compound events (taking one counter from each bag).

Key Terms and Formulas

• Probability Tree: A diagram showing all possible outcomes and their probabilities.

• Multiplication Rule:

• Probability of an event:

Step-by-Step Guidance

1. Calculate the probability of picking a blue counter from Bag A:

2. Calculate the probability of picking a blue counter from Bag B:

3. To find the probability Tina takes two blue counters, multiply the probabilities from each bag:

4. Set up the multiplication, but do not compute the final value yet.

Try solving on your own before revealing the answer!

Q2. Hannah plays one game of chess and one game of backgammon. Probability she wins chess is 0.6, probability she wins backgammon is 0.7.

Background

Topic: Probability Trees and Independent Events

This question tests your ability to use probability trees and calculate the probability of winning both games, assuming independence.

Key Terms and Formulas

• Independent Events: Events where the outcome of one does not affect the other.

• Multiplication Rule:

Step-by-Step Guidance

1. Identify the probability Hannah wins chess:

2. Identify the probability Hannah wins backgammon:

3. Multiply these probabilities to find the chance she wins both:

4. Set up the multiplication, but do not compute the final value yet.

Try solving on your own before revealing the answer!

Q3. Rachel has two bags. First bag: 4 red, 6 green balls. Second bag: 3 red, 5 green balls. She takes one ball from each bag at random.

Background

Topic: Probability Trees and Compound Probability

This question tests your ability to use probability trees to calculate the probability of taking two green balls.

Key Terms and Formulas

• Probability of an event:

• Multiplication Rule:

Step-by-Step Guidance

1. Calculate the probability of picking a green ball from the first bag:

2. Calculate the probability of picking a green ball from the second bag:

3. Multiply these probabilities:

4. Set up the multiplication, but do not compute the final value yet.

Try solving on your own before revealing the answer!

Q4. Jo is going to play one tennis match and one squash match. The probability she will win the tennis match is 0.4. The probability she will win the squash match is 0.5.

Background

Topic: Probability Trees and Independent Events

This question tests your ability to use probability trees and calculate the probability of winning both matches.

Key Terms and Formulas

• Multiplication Rule:

Step-by-Step Guidance

1. Identify the probability Jo wins tennis:

2. Identify the probability Jo wins squash:

3. Multiply these probabilities:

4. Set up the multiplication, but do not compute the final value yet.

Try solving on your own before revealing the answer!

Q5. Each day Paul wears either a black tie or a red tie to work. On any day the probability he wears a black tie is 0.5. Complete the probability tree diagram for Monday and Tuesday. Work out the probability Paul wears different coloured ties on Monday and Tuesday.

Background

Topic: Probability Trees and Compound Probability

This question tests your ability to use probability trees to calculate the probability of two events (tie color) over two days.

Key Terms and Formulas

• Probability of an event:

• Multiplication Rule:

Step-by-Step Guidance

1. Probability Paul wears a black tie on Monday:

2. Probability Paul wears a red tie on Monday:

3. For each Monday outcome, calculate the probability of wearing the opposite color on Tuesday: and

4. Add these two probabilities to find the total probability Paul wears different colored ties.

Try solving on your own before revealing the answer!

Q6. Jon plays a game where he can win, draw, or lose. Probability Jon wins any game is 0.5. Probability Jon draws any game is 0.3. Jon plays two games. Work out the probability Jon wins both games.

Background

Topic: Probability Trees and Compound Probability

This question tests your ability to use probability trees for events with more than two outcomes and calculate compound probabilities.

Key Terms and Formulas

• Probability of an event:

• Multiplication Rule:

Step-by-Step Guidance

1. Probability Jon wins the first game:

2. Probability Jon wins the second game:

3. Multiply these probabilities:

4. Set up the multiplication, but do not compute the final value yet.

Try solving on your own before revealing the answer!

Q7. Bradley gets the bus on Saturday and Sunday. The probability that Bradley’s bus will be late on any day is 0.2. Work out the probability that Bradley’s bus is late on at least one of these days.

Background

Topic: Probability Trees and Complement Rule

This question tests your ability to use probability trees and the complement rule to find the probability of 'at least one' event.

Key Terms and Formulas

• Complement Rule:

• Multiplication Rule:

Step-by-Step Guidance

1. Probability bus is not late on a day:

2. Probability bus is not late on both days:

3. Probability bus is late on at least one day:

4. Set up the subtraction, but do not compute the final value yet.

Try solving on your own before revealing the answer!

Q8. Felicity is going to play one game of chess and one game of draughts. Probability she will win chess is 0.8. Probability she will win draughts is 0.6. Work out the probability that Felicity will win exactly one of these games.

Background

Topic: Probability Trees and Exclusive Events

This question tests your ability to calculate the probability of winning exactly one game (not both, not none).

Key Terms and Formulas

• Probability of winning chess and losing draughts:

• Probability of losing chess and winning draughts:

• Add these two probabilities for 'exactly one win'.

Step-by-Step Guidance

1. Calculate

2. Calculate

3. Add these two probabilities:

4. Set up the addition, but do not compute the final value yet.

Try solving on your own before revealing the answer!

Q9. Mimi has two bags. First bag: 3 red, 7 green balls. Second bag: 4 red, 5 green balls. Mimi takes one ball from each bag at random. Work out the probability that Mimi takes two green balls.

Background

Topic: Probability Trees and Compound Probability

This question tests your ability to use probability trees to calculate the probability of taking two green balls.

Key Terms and Formulas

• Probability of an event:

• Multiplication Rule:

Step-by-Step Guidance

1. Calculate the probability of picking a green ball from the first bag:

2. Calculate the probability of picking a green ball from the second bag:

3. Multiply these probabilities:

4. Set up the multiplication, but do not compute the final value yet.

Try solving on your own before revealing the answer!

Q10. Lola plays a game where she can win, draw, or lose. Probability Lola wins any game is 0.6. Probability Lola draws any game is 0.1. Lola plays two games. Work out the probability Lola wins exactly one game.

Background

Topic: Probability Trees and Exclusive Events

This question tests your ability to calculate the probability of winning exactly one game (not both, not none).

Key Terms and Formulas

• Probability Lola wins first and not second:

• Probability Lola does not win first and wins second:

• Add these two probabilities for 'exactly one win'.

Step-by-Step Guidance

1. Calculate

2. Calculate

3. Add these two probabilities:

4. Set up the addition, but do not compute the final value yet.

Try solving on your own before revealing the answer!