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7.04 Probability and tree diagrams

Interactive practice questions

Three fair coins are tossed.

a

Find the probability of obtaining at least one head.

b

What is the probability of obtaining TTH in this sequence?

c

What is the probability of obtaining THH in this sequence?

Medium
1min

A bag contains four marbles - red, green, blue and yellow. Eileen randomly selects a marble, returns the marble to the bag and selects another marble.

Medium
2min

An ice-cream shop offers one flavour of ice-cream at a discounted price each day. There are $6$6 flavours for the owner to choose from, that could be discounted. $3$3 of the flavours are sorbet and the other $3$3 are gelato. The three sorbet flavours are raspberry (R), lemon (L) and chocolate (C). The three gelato flavours are vanilla (V), mint (M) and chocolate (C). Each decision has equal probability.

Medium
1min

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
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Outcomes

4.1.8

use a sample space to determine the probability of outcomes for an experiment

4.1.9

use arrays or tree diagrams to determine the outcomes and the probabilities for experiments

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