Dean Chalmers and Julian Gilbey Solutions for Chapter: Practice Exam-Style Paper, Exercise 1: PRACTICE EXAM-STYLE PAPER

Meng buys a packet of nine different bracelets. She takes two for herself and then shares the remainder at random between her two best friends.
If the two friends receive at least one bracelet each, find the probability that one friend receives exactly one bracelet more than the other.

The following histogram summarises the total distance covered on each of $123$ taxi journeys provided for customers of Jollicabs during the weekend.

Find the upper boundary of the range of distances covered on these journeys.

The following histogram summarises the total distance covered on each of $123$ the taxi journeys provided for customers of Jollicabs during the weekend.

Estimate the number of journeys that covered a total distance from $8$ to $13$ kilometres.

The following histogram summarises the total distance covered on each of 123 taxi journeys provided for customers of Jollicabs during the weekend.

Calculate an estimate of the mean distance covered on these $123$ journeys.

In each of a series of independent trials, a success occurs with a constant probability of $0.9.$

The probability that none of the first $n$ trials results in a failure is less than $0.3.$ Find the least possible value of $n.$

In each of a series of independent trials, a success occurs with a constant probability of $0.9.$

Use a suitable approximation to calculate an estimate of the probability that fewer than $70$ successes occur in $80$ trials.

The following stem-and-leaf diagram shows the number of shots taken by $10$ players to complete a round of golf.

$\begin{array}{llllll}6& 1& y& & \mathrm{Key}: 6\mid 1& \\ 7& 0& 1& 2& x& \mathrm{represents} \\ 8& 0& 1& 9& 9& 61 \mathrm{shots} \end{array}$

Given that the whisker is $16.8 \mathrm{cm}$ long, find the value of $b,$ if the width of the box is $b \mathrm{cm}.$

To conduct an experiment, a student must fit three capacitors into a circuit. He has eight to choose from but, unknown to him, two are damaged. He fits three randomly selected capacitors into the circuit. The random variable $X$ is the number of damaged capacitors in the circuit.

The student discovers that exactly one of the capacitors in the circuit is damaged but he does not know which one. He removes one capacitor from the circuit and replaces it with one from the box, both selected at random. Find the probability that the circuit now has at least one damaged capacitor in it.