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.
What is the probability that a randomly chosen student is in year 9 and does not like maths?
What is the overall proportion of students who do not like maths?
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.
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.
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%.