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6.05 Conditional probability and independent events

Interactive practice questions

A container holds four counters coloured red, blue, green and yellow.

a

Draw a tree diagram representing all possible outcomes when two draws are done, and the first counter is replaced before the second draw.

b

Draw a tree diagram representing all possible outcomes if two draws are done, and the first counter is not replaced before the next draw.

Easy
1min

There are $4$4 green counters and $8$8 purple counters in a bag. What is the probability of choosing a green counter, not replacing it, then choosing a purple counter?

Easy
1min

A card is randomly selected from a normal deck of cards, and then returned to the deck. The deck is shuffled and another card is selected.

Easy
< 1min

In a lottery, a numbered ball is selected from a basket. The result is recorded and the ball is set aside. Several more numbers are taken from the basket in this way until the lottery is complete.

Are the selections of the numbers independent or dependent?

Easy
< 1min
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Outcomes

1.3.13

understand the notion of a conditional probability and recognise and use language that indicates conditionality

1.3.14

use the notation 𝑃(𝐴|𝐵) and the formula 𝑃(𝐴∩𝐵) =𝑃(𝐴|𝐵)𝑃(𝐵)

1.3.15

understand the notion of independence of an event A from an event B, as defined by P(A|B)=P(A)

1.3.16

establish and use the formula 𝑃(𝐴∩𝐵) = 𝑃(A)𝑃(𝐵) for independent events 𝐴 and 𝐵, and recognise the symmetry of independence

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