NZ Level 8 (NZC) Level 3 (NCEA) [In development] Conditional Probability - Sample Spaces

## Interactive practice questions

There are four cards marked with the numbers $2$2, $5$5, $8$8, and $9$9. They are put in a box. Two cards are selected at random one after the other without replacement to form a two-digit number.

a

Draw a tree diagram to illustrate all the possible outcomes.

b

How many different two-digit numbers can be formed.

c

What is the probability of obtaining a number less than $59$59?

d

What is the probability of obtaining an odd number?

e

What is the probability of obtaining an even number?

f

What is the probability of obtaining a number greater than $90$90?

g

What is the probability that the number formed is divisible by 5?

Easy
Approx 4 minutes

The Venn diagram shown shows the number of students in a school playing the sports of Rugby League, Rugby Union, both or neither.

Bag A contains $15$15 red marbles and $10$10 blue marbles, while bag B contains $20$20 red marbles and $25$25 blue marbles. If Eileen is to select a marble by first selecting a bag at random and then selecting a random marble from that bag:

Han draws two cards without replacement from a set of cards numbered 1 to 4 to create a 2-digit number, for instance if they draw a $1$1 then a $2$2 the number $12$12 is formed.

### 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