Natasha Awada, Paul La Rondie, Laurie Buchanan and, Jill Stevens Solutions for Chapter: Valid Comparisons and Informed Decisions: Probability Distributions, Exercise 39: Chapter review

In a game a player rolls a biased tetrahedral (four-faced) die. The probability of each possible score is shown below.

Find the probability of a total score of six after two rolls.

A game involves spinning two spinners. One is numbered $1,2,3,4$. The other is numbered $2,2,4,4$. Each spinner is spun once and the number on each is recorded. Let $P$ be the product of the numbers on the spinners. Write down all the possible values for $P$.

A game involves spinning two spinners. One is numbered $1,2,3,4$. The other is numbered $2,2,4,4$. Each spinner is spun once and the number on each is recorded. Let $P$ be the product of the numbers on the spinners. Find the probability of each value of $P$.

A game involves spinning two spinners. One is numbered $1,2,3,4$. The other is numbered $2,2,4,4$. Each spinner is spun once and the number on each is recorded. Let $P$ be the product of the numbers on the spinners. Find the expected value of $P$.

A game involves spinning two spinners. One is numbered $1,2,3,4$. The other is numbered $2,2,4,4$. Each spinner is spun once and the number on each is recorded. Let $P$ be the product of the numbers on the spinners. A mathematician determines the amount of pocket money to give his son each week by getting him to play the game on Monday morning. If the son spins and the product is greater than $10$, then the boy gets $\pounds 10$. Otherwise, the boy gets $\pounds 5$. Find how much in total should the boy expect to get after $10$ weeks of playing the game.

On a train, $\frac{1}{3}$ of the passengers are listening to music. Five passengers are chosen at random. Find the probability that exactly three passengers are listening to music.

When Abhinav plays a game at a fair, the probability that he wins a prize is $0.1$. He plays the game twice. Let $X$ denote the total number of prizes that he wins. Assuming that the games are independent, find $E\left(X\right)$.

The time taken for Samuel to get to school each morning is normally distributed with a mean of $\mu$ $\mathrm{minutes}$ and a standard deviation of $2$ $\mathrm{minutes}$. The probability that the journey takes more than $35$ $\mathrm{minutes}$ is $0.2$. Find the value of $\mu$ (Write the answer up to one decimal place in $\mathrm{minutes}$) [Use GCD calculator]