CIE Oct 2020 9709 Prob & Stats 1 Paper 52 (pdf)
- A fair six-sided die, with faces marked 1, 2, 3, 4, 5, 6, is thrown repeatedly until a 4 is obtained.
(a) Find the probability that obtaining a 4 requires fewer than 6 throws
On another occasion, the die is thrown 10 times.
(b) Find the probability that a 4 is obtained at least 3 times
- A bag contains 5 red balls and 3 blue balls. Sadie takes 3 balls at random from the bag, without
replacement. The random variable X represents the number of red balls that she takes.
(a) Show that the probability that Sadie takes exactly 1 red ball is 15/56.
(b) Draw up the probability distribution table for X
(c) Given that EX(X) = 15/8, find Var(X)
- Pia runs 2 km every day and her times in minutes are normally distributed with mean 10.1 and standard
(a) Find the probability that on a randomly chosen day Pia takes longer than 11.3 minutes to run
(b) On 75% of days, Pia takes longer than t minutes to run 2 km. Find the value of t
(c) On how many days in a period of 90 days would you expect Pia to take between 8.9 and
11.3 minutes to run 2 km?
- In a certain country, the weather each day is classified as fine or rainy. The probability that a fine day
is followed by a fine day is 0.75 and the probability that a rainy day is followed by a fine day is 0.4.
The probability that it is fine on 1 April is 0.8. The tree diagram below shows the possibilities for the
weather on 1 April and 2 April.
(a) Complete the tree diagram to show the probabilities.
(b) Find the probability that 2 April is fine.
Let X be the event that 1 April is fine and Y be the event that 3 April is rainy.
(c) Find the value of P(X ∪ Y)
(d) Find the probability that 1 April is fine given that 3 April is rainy
- The following table gives the weekly snowfall, in centimetres, for 11 weeks in 2018 at two ski resorts,
Dados and Linva.
(a) Represent the information in a back-to-back stem-and-leaf diagram
(b) Find the median and the interquartile range for the weekly snowfall in Dados.
(c) The median, lower quartile and upper quartile of the weekly snowfall for Linva are 12, 9 and
32 cm respectively. Use this information and your answers to part (b) to compare the central
tendency and the spread of the weekly snowfall in Dados and Linva.
- Mr and Mrs Ahmed with their two children, and Mr and Mrs Baker with their three children, are
visiting an activity centre together. They will divide into groups for some of the activities.
(a) In how many ways can the 9 people be divided into a group of 6 and a group of 3?
5 of the 9 people are selected at random for a particular activity.
(b) Find the probability that this group of 5 people contains all 3 of the Baker children.
All 9 people stand in a line.
(c) Find the number of different arrangements in which Mr Ahmed is not standing next to Mr Baker
(d) Find the number of different arrangements in which there is exactly one person between
Mr Ahmed and Mr Baker
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