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New Zealand
Level 8 - NCEA Level 3

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.


Draw a tree diagram to illustrate all the possible outcomes.


How many different two-digit numbers can be formed.


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


What is the probability of obtaining an odd number?


What is the probability of obtaining an even number?


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


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

Approx 4 minutes
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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.



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


Apply probability concepts in solving problems

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