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5.06 Independent events and data

Interactive practice questions

Ursula takes a bus to the station and then immediately gets on a train to work. Is the probability of her missing the train independent or dependent on her missing her bus?

Dependent

A

Independent

B
Easy
< 1min

If two events are independent, then

$P$P$($($A$A and $B$B$)$) $=$=

Easy
< 1min

The probability that Ursula, Jimmy and Bianca get permission to go on their school trip are $0.5$0.5, $0.7$0.7 and $0.3$0.3, respectively. What is the probability that at least one of them gets permission?

Medium
2min

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
5min
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Outcomes

1.3.3.3

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

1.3.3.4

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

1.3.3.5

use relative frequencies obtained from data as point estimates of conditional probabilities and as indications of possible independence of events

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