Dean Chalmers and Julian Gilbey Solutions for Chapter: The Binomial and Geometric Distributions, Exercise 10: END-OF-CHAPTER REVIEW EXERCISE 7

Four ordinary fair dice are rolled. Find the probability that the four numbers obtained have a sum of $22$ ?

Four ordinary fair dice are rolled. The four dice are rolled on eight occasions. Find the probability that the four numbers obtained have a sum of $22$ on at least two of these occasions.

When a certain driver parks their car in the evenings, they are equally likely to remember or to forget to switch off the headlights. Find the probability that on the next $16$ occasions that they park their car in the evening, they forget to switch off the headlights: $14$ more times than they remember to switch them off

When a certain driver parks their car in the evenings, they are equally likely to remember or to forget to switch off the headlights. Find the probability that on the next $16$ occasions that they park their car in the evening, they forget to switch off the headlights: at least $12$ more times than they remember to switch them off.

Gina has been observing students at a university. Her data indicate that $60\%$of the males and $70\%$ of the females are wearing earphones at any given time. She decides to interview randomly selected students and to interview males and females alternately. Use Gina's observation data to find the probability that the first person not wearing earphones is the third male interviewed, given that she first interviews: a female and state any assumptions made about the wearing of earphones in your calculations

Gina has been observing students at a university. Her data indicate that $60\%$of the males and $70\%$ of the females are wearing earphones at any given time. She decides to interview randomly selected students and to interview males and females alternately. Use Gina's observation data to find the probability that the first person not wearing earphones is the third male interviewed, given that she first interviews: a male who is wearing earphones. and state any assumptions made about the wearing of earphones in your calculations

In Restaurant Bijoux $13\%$ of customers rated the food as 'poor', $22\%$ of customers rated the food as 'satisfactory' and $65\%$ rated it as 'good'. A random sample of $12$ customers who went for a meal at Restaurant Bijoux was taken. Find the probability that more than $2$ and fewer than $12$ of them rated the food as 'good'.

In Restaurant Bijoux $13\%$ of customers rated the food as 'poor', $22\%$ of customers rated the food as 'satisfactory' and $65\%$ rated it as 'good'. On a separate occasion, a random sample of $n$ customers who went for a meal at the restaurant was taken. Find the smallest value of $n$ for which the probability that at least $1$ person will rate the food as 'poor' is greater than $0.95$.