Analysis and Approaches for IBDP Maths Ebook 2 | Page 238

Your Practice Set – Analysis and Approaches for IBDP Mathematics
Exercise 74
1. In an airport, there are only two international airlines available. CAN Air has 50 flights a
day and INT Air has 36 flights a day. Passengers flying with CAN Air have an 11%
probability of having a late departure and passengers flying with INT Air have a 17%
probability of having a late departure.
(a)
(b)
Find the probability that a flight departs late.
[3]
A randomly chosen flight departs late. Find the probability that the flight belongs
to CAN Air.
[3]
2. Zoe goes to school by bus every day. When it is raining, the probability that the bus is
late is 11
3
. When it is not raining, the probability that the bus is late is
40 40 . The
probability of a bus being late is 0.121.
(a)
(b)
Find the probability that it rains on a particular day.
[3]
On one particular day the bus is not late. Find the probability that it is raining on
that day.
[3]
3. In a population of cats, 1.5% are known to have a particular disease. A test is developed
for the disease that gives a positive result for a cat that does have the disease in 100 p %
of cases. It is also known that the test gives a positive result for a cat that does not have
the disease in p % of cases. A cat is chosen at random from the population, and it is
given that the probability that the cat tests positive for the disease is 0.024353.
(a) Find the value of p .
(b)
Given that the cat tests positive for the disease, find the probability that the cat
does not have the disease.
[3]
[3]
4. In a particular week, Florence and Givanni pick a night at random on which they will
watch a movie. If they choose a weekday night, the probability that they watch a Korean
movie is 0.675 and if they choose any other night the probability that they watch a
Korean movie is 0.465. Given that in the week they watched a Korean movie, find the
probability that they chose a non-weekday night.
[4]
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