New Zealand
Level 8 - NCEA Level 3

# Mixed Probability and Sample Spaces

## Interactive practice questions

Buzz can’t remember the combination for his lock, but he knows it is a three digit number and contains the digits $6$6, $8$8 and $9$9.

a

List all possible locker combinations that Buzz should try.

Write all the combinations on the same line, separated by commas.

b

State the total number of possible outcomes.

c

If Buzz is correct that the combination includes $6$6, $8$8 and $9$9, what is the probability the combination starts with $6$6?

d

What is the probability the combination starts with $6$6 and ends with $8$8?

e

What is the probability the combination starts with $6$6 or ends with $9$9?

Easy
Approx 3 minutes

Luke can’t remember the order of his PIN for his EFTPOS card, but he knows it contains the digits in $2853$2853.

The following two spinners are spun and the result of each spin is recorded.

The following spinner is spun and a normal six-sided die is rolled. The result of each is recorded.

### 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