Dean Chalmers and Julian Gilbey Solutions for Chapter: Probability, Exercise 9: EXERCISE 4F

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 $m$.

Two children are selected from a group in which there are $10$ more boys than girls. Given that there are $756$ equiprobable ordered selections that can occur, find the probability that two boys or two girls are selected.    [correct up to three decimal places]

There is a $43\%$ chance that Riya meets her friend Jasmine when she travels to work. Given that Riya walks to work and does not meet Jasmine $30\%$ of the time, and that she travels to work by a different method and meets Jasmine $25\%$ of the time, find the probability that Riya walks to work on any particular day.

Aaliyah buys a randomly selected magazine that contains a crossword puzzle on five randomly chosen days of each week. On $84\%$ of the occasions that she buys a magazine, she attempts its crossword, which she manages to complete $60\%$ of the time. Find the probability that, on any particular day, Aaliyah does not complete the crossword in a magazine.