A number between $10$ and $100$ inclusive is selected at random. Find the probability that the number is a multiple of $5$, given that none of its digits is a $5$ .

Three of $\mathrm{Mr}$ Jumbillo's seven children, who include one set of twins, are selected at random.

Calculate the probability that exactly one of the twins is selected.

Three of Mr Jumbillo's seven children, who include one set of twins, are selected at random.

Given that exactly three of the children are girls, find the probability that the selection of three children contains more girls than boys.

Anya calls Zara once each evening before she goes to bed. She calls Zara's mobile phone with probability $0.8$ or her landline. The probability that Zara answers her mobile phone is $0.74$, and the probability that she answers her landline is $y$. This information is displayed in the tree diagram shown.

Given that Zara answers $68\%$ of Anya's calls, find the value of $y$.

Anya calls Zara once each evening before she goes to bed. She calls Zara's mobile phone with probability $0.8$ or her landline. The probability that Zara answers her mobile phone is $0.74$, and the probability that she answers her landline is $y$. This information is displayed in the tree diagram shown.

Given that Anya's call is not answered, find the probability that it is made to Zara's landline.

Every Friday, Arif of fers to take his sons to the beach or to the park. The sons refuse an offer to the beach with probability $0.65$ and accept an offer to the park with probability $0.85$. The probability that Arif offers to take them to the beach is $x$. This information is shown in the tree diagram.

Find the value of $x$, given that $33\%$ of Arif's offers are refused.

Every Friday, Arif offers to take his sons to the beach or to the park. The sons refuse an offer to the beach with probability $0.65$ and accept an offer to the park with probability $0.85$. The probability that Arif offers to take them to the beach is $x$. This information is shown in the tree diagram.

Given that Arif's offer is accepted, probability that he offers to take his sons to the park is $\frac{0.85-0.85x}{0.85-mx}$. Find $m$.