Every Friday evening Sunil either cooks a meal for Mina or buys her a take-away meal. The probability that he buys a takeaway meal is $0.24.$ If Sunil cooks the meal, the probability that Mina enjoys it is $0.75,$ and if he buys her a takeaway meal, the probability that she does not enjoy it is $x.$ This information is shown in the following tree diagram.

The probability that Sunil buys a take-away meal and Mina enjoys it is $0.156.$

Find the value of $x.$

Every Friday evening Sunil either cooks a meal for Mina or buys her a take-away meal. The probability that he buys a takeaway meal is $0.24.$ If Sunil cooks the meal, the probability that Mina enjoys it is $0.75,$ and if he buys her a takeaway meal, the probability that she does not enjoy it is $x.$ This information is shown in the following tree diagram.

The probability that Sunil buys a take-away meal and Mina enjoys it is $0.156.$

Given that Mina does not enjoy her Friday meal, find the probability that Sunil cooked it. (Round off to three decimal places)

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 $0.9.$

State the most likely trial in which the first success will occur.

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 median number of shots is $74.5$ and that the mean number of shots is $75.4,$ find the value of $x$ and of $y.$

The numbers of golf shots are summarised in a box-and-whisker diagram, as shown.