Dean Chalmers and Julian Gilbey Solutions for Chapter: Probability Distributions, Exercise 7: END-OF-CHAPTER REVIEW EXERCISE 6

Four students are to be selected at random from a group that consists of seven boys and $x$ girls. The variables $B$ and $G$ are, respectively, the number of boys selected and the number of girls selected.

Given that $G\ne 3,$ find the probability that $G=4.$

A box contains $2$ green apples and $2$ red apples. Apples are taken from the box, one at a time, without replacement. When both red apples have been taken, the process stops. The random variable $X$ is the number of apples which have been taken when the process stops.

Show that $P\left(X=3\right)=\frac{1}{3}$

A box contains $2$ green apples and $2$ red apples. Apples are taken from the box, one at a time, without replacement. When both red apples have been taken, the process stops. The random variable $X$ is the number of apples which have been taken when the process stops.

Draw up the probability distribution table for $X.$ Another box contains $2$ yellow peppers and $5$ orange peppers. Three peppers are taken from the box without replacement.

A box contains $2$ green apples and $2$ red apples. Apples are taken from the box, one at a time, without replacement. When both red apples have been taken, the process stops. The random variable $X$ is the number of apples which have been taken when the process stops.

Given that at least $2$ of the peppers taken from the box are orange, find the probability that all $3$ peppers are orange.

In a particular discrete probability distribution the random variable $X$ takes the value $\frac{120}{r}$ with probability $\frac{r}{45},$ where $r$ takes all integer values from $1$ to $9$ inclusive.
Show that $P\left(X=40\right)=\frac{1}{15}.$

In a particular discrete probability distribution the random variable $X$ takes the value $\frac{120}{r}$ with probability $\frac{r}{45},$ where $r$ takes all integer values from $1$ to $9$ inclusive.
Construct the probability distribution table for $X.$

In a particular discrete probability distribution the random variable $X$ takes the value $\frac{120}{r}$ with probability $\frac{r}{45},$ where $r$ takes all integer values from $1$ to $9$ inclusive.

Which is the modal value of $X$ ?

In a particular discrete probability distribution the random variable $X$ takes the value $\frac{120}{r}$ with probability $\frac{r}{45},$ where $r$ takes all integer values from $1$ to $9$ inclusive.

Find the probability that $X$ lies between $18$ and $100.$