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India
Class XI

Law of Total Probability

Interactive practice questions

At a particular school, there are $270$270 students in year 9 and $180$180 students in year 10. $20%$20% of the year 9 students and $45%$45% of the year 10 students like maths.

a

What is the probability that a randomly chosen student is in year 9 and does not like maths?

b

What is the overall proportion of students who do not like maths?

Easy
6min

The probability that it will rain in Penrith on a Saturday is $0.27$0.27. If it does rain on a Saturday, then the probability that it will rain on the Sunday is $0.78$0.78. But if it doesn't rain on a Saturday, the probability that it will rain on the Sunday is $0.4$0.4.

Easy
5min

In the month of June, it rains on average $17$17 days of the month in Perth. It if rains, the chance that Carl catches the bus to work is $\frac{3}{10}$310. If it doesn’t rain, the chance that Carl catches the bus to work is $\frac{9}{10}$910.

Medium
6min

Jo and Em are often caught for talking in class.

The probability that Jo starts a conversation is $70%$70%. If Jo starts talking, the chance that Em responds is $80%$80%. If Jo doesn’t start a conversation, the chance that Em does is $10%$10%.

Medium
5min
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Outcomes

11.SP.P.1

Random experiments: Outcomes, sample spaces (set representation). Events: Occurrence of events, ‘not’, ‘and’ & ‘or’ events, exhaustive events, mutually exclusive events. Axiomatic (set theoretic) probability, connections with the theories of earlier classes. Probability of an event, probability of ‘not’, ‘and’ & ‘or’ events.

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