StudentAidProbability & Statistics 1 — Variant 3
A Level Mathematics · 9709/53 · May/June 2020
Questions
4 of 7 questions shown here, checked against the paper. The others are in the PDF above — they contain diagrams or maths we could not yet verify, and we would rather show you the original than a transcription we are not sure of.
1
Juan goes to college each day by any one of car or bus or walking. The probability that he goes by car is , the probability that he goes by bus is and the probability that he walks is . When Juan goes by car, the probability that he arrives early is . When he goes by bus, the probability that he arrives early is . When he walks he always arrives early.
1(a)
[2]
Draw a fully labelled tree diagram to represent this information.
1(b)
[4]
Find the probability that Juan goes to college by car given that he arrives early.
2
In a certain large college, of students own a car.
2(a)
[1]
3 students from the college are chosen at random. Find the probability that all 3 students own a car.
2(b)
[3]
16 students from the college are chosen at random. Find the probability that the number of these students who own a car is at least and at most .
3
In a certain town, the time, hours, for which people watch television in a week has a normal distribution with mean hours and standard deviation hours.
3(a)
[2]
Find the probability that a randomly chosen person from this town watches television for less than hours in a week.
3(b)
[3]
Find the value of such that .
4
A fair four-sided spinner has edges numbered . A fair three-sided spinner has edges numbered . Each spinner is spun and the number on the edge on which it comes to rest is noted. The random variable is the sum of the two numbers that have been noted.
4(a)
[3]
Draw up the probability distribution table for .
4(b)
[3]
Find .
Published by Cambridge Assessment International Education. Reproduced for study use.