Liam is playing two games. He is equally likely to win each game. The probability that Liam will win at least one of the games is 80%.

Which of the following is closest to the probability that Liam will win both games?

• 31%

• 40%

• 55%

• 64%

Answer explanation

2022 HSC Q9

In a bag there are 3 six-sided dice. Two of the dice have faces marked 1, 2, 3, 4, 5, 6.

The other is a special die with faces marked 1, 2, 3, 5, 5, 5. One die is randomly selected and tossed.

What is the probability that the die shows a 5?

Mathematical Equivalence

ON

Answer explanation

2022 HSC Q15a (1 mark)

In a bag there are 3 six-sided dice. Two of the dice have faces marked 1, 2, 3, 4, 5, 6.

The other is a special die with faces marked 1, 2, 3, 5, 5, 5. One die is randomly selected and tossed.

Given that the die shows a 5, what is the probability that it is the special die?

Mathematical Equivalence

ON

Answer explanation

2022 HSC Q15b (1 mark)

There are 8 chocolates in a box. Three have peppermint centres (P) and five have caramel centres (C).

Kim randomly chooses a chocolate from the box and eats it. Sam then randomly chooses and eats one of the remaining chocolates.

A partially completed probability tree is shown.

What is the probability that Kim and Sam choose chocolates with different centres?

Answer explanation

2021 HSC Q6

History and Geography are two of the subjects students may decide to study. For a group of 40 students, the following is known.
• 7 students study neither History nor Geography

• 20 students study History
• 18 students study Geography

2.  A student is chosen at random. By using a Venn diagram, or otherwise, find the probability that the student studies both History and Geography

Mathematical Equivalence

ON

Answer explanation

2020 HSC Q14a (2 marks)

History and Geography are two of the subjects students may decide to study. For a group of 40 students, the following is known.
• 7 students study neither History nor Geography

• 20 students study History
• 18 students study Geography

2.  A student is chosen at random. Given that the student studies Geography, what is the probability that the student does NOT study History?

Mathematical Equivalence

ON

Answer explanation

2020 HSC Q14b (1 mark)

History and Geography are two of the subjects students may decide to study. For a group of 40 students, the following is known.
• 7 students study neither History nor Geography

• 20 students study History
• 18 students study Geography

2.  Two different students are chosen at random, one after the other. What is the probability that the first student studies History and the second student does
   NOT study History?

Mathematical Equivalence

ON

Answer explanation

2020 HSC Q14c (2 marks)

A game is played by tossing an ordinary 6-sided die and an ordinary coin at the same time. The game is won if the uppermost face of the die shows an even number or the uppermost face of the coin shows a tail (or both).

What is the probability of winning this game?

Answer explanation

2019 HSC Q6

6. A bag contains 5 green beads and 7 purple beads. Two beads are selected at random, without replacement.

   What is the probability that the two beads are the same colour?

Mathematical Equivalence

ON

Answer explanation

2019 HSC Q11f (2 marks)

The probability that a person chosen at random has red hair is 0.02 .

2. Two people are chosen at random.

3. What is the probability that at least ONE has red hair?

4. (answer to 4 decimal places)

Mathematical Equivalence

ON

Answer explanation

2019 HSC Q 15(d)(i) (2 marks)