New Zealand
Level 8 - NCEA Level 3

# Conditional Probability - Combinations

## Interactive practice questions

A student is choosing two units to study at university: a language and a science unit. They have $4$4 languages and $7$7 science units to choose from.

a

If they choose one of each, what is the total number of combinations of choices?

b

If Italian is one of the languages they can choose from, what is the probability they choose Italian as their language?

c

French is one of the available languages. What is the probability they choose French as their language given that they choose Chemistry as their science unit?

Easy
Approx 2 minutes

For breakfast each morning, Marge eats porridge, toast or cereal. With that she will either drink orange juice, tea or hot chocolate.

A netball coach is choosing players for the Goal Keeper and Goal Defence positions.

For the Goal Keeper position she can choose from Beth, Amy, Joy and Tara. For the Goal Defence position she can choose from Eve, Cara, Daisy, Kim and Liz.

The selection for each position is made independently.

In the Have Sum Fun competition, a teacher needs to make a team of $4$4 people and another team of $3$3 people.

For the larger team the teacher has $5$5 students to choose from, including Jack and Julia.

For the smaller team, the teacher has $4$4 students to choose from, including Alvin.

### Outcomes

#### S8-4

Investigate situations that involve elements of chance: A calculating probabilities of independent, combined, and conditional events B calculating and interpreting expected values and standard deviations of discrete random variables C applying distributions such as the Poisson, binomial, and normal

#### 91585

Apply probability concepts in solving problems