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10.05 Solving problems with probability

Interactive practice questions

Consider the following probability Venn Diagram:

Find $P$P$($($A$A$|$|$B$B$)$). Express your answer as a fully reduced fraction.

Easy
1min

Given that $P\left(A\cap B\right)=$P(AB)=$0.2$0.2 and $P\left(A\cap B'\right)=$P(AB)=$0.3$0.3.

Medium
4min

Three cards labelled $\editable{2}$2, $\editable{3}$3 and $\editable{4}$4 are placed face down on a table. Two of the cards are selected randomly to form a two-digit number. The outcomes are displayed in the following probability tree.

Medium
2min

Students were asked what they are allergic to. The table shows the results.

If a student is chosen at random, what is the probability that they:

Medium
3min
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Outcomes

VCMSP347

Describe the results of two- and three-step chance experiments, both with and without replacements, assign probabilities to outcomes and determine probabilities of events. Investigate the concept of independence.

VCMSP348

Use the language of ‘if ....then, ‘given’, ‘of’, ‘knowing that’ to investigate conditional statements and identify common mistakes in interpreting such language.

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