A survey was carried out regarding the school dress code. The two-way table shows the results:

	Should have dress code	Should not have dress code	Total
Middle school		$30$	$45$
High school	$40$
Total	$55$	$110$

Copy and complete the table

A survey was carried out regarding the school dress code. The two-way table shows the results:

Use Theorems $2$ to determine whether Type of school and wanting a dress code are independent events

The table shows the occurrence of diabetes in $200$ people.

$\begin{array}{lcc}& \text{ Diabetes }& \text{ No diabetes }\\ \text{ Not overweight }& 10& 90\\ \text{ Overweight }& 35& 65\\ & & \end{array}$

Let $D$ be the event 'has diabetes'.
Let $N$ be the event 'not overweight'.

From the table find $P\left(D\right)$?

The table shows the occurrence of diabetes in $200$ people.

$\begin{array}{lcc}& \text{ Diabetes }& \text{ No diabetes }\\ \text{ Not overweight }& 10& 90\\ \text{ Overweight }& 35& 65\\ & & \end{array}$

Let $D$ be the event 'has diabetes'.
Let $N$ be the event 'not overweight'.

From the table find $P\left(N\right)$?

The table shows the occurrence of diabetes in $200$ people.

$\begin{array}{lcc}& \text{ Diabetes }& \text{ No diabetes }\\ \text{ Not overweight }& 10& 90\\ \text{ Overweight }& 35& 65\\ & & \end{array}$

Let $D$ be the event 'has diabetes'.
Let $N$ be the event 'not overweight'.

From the table find $\mathrm{P}(D\mid N)$?

The table shows the occurrence of diabetes in $200$ people.

$\begin{array}{lcc}& \text{ Diabetes }& \text{ No diabetes }\\ \text{ Not overweight }& 10& 90\\ \text{ Overweight }& 35& 65\\ & & \end{array}$

Let $D$ be the event 'has diabetes'.
Let $N$ be the event 'not overweight'.

From the table find $\mathrm{P}\left(D\mid N^{\text{'}}\right)$?

The table shows the occurrence of diabetes in $200$ people.

$\begin{array}{lcc}& \text{ Diabetes }& \text{ No diabetes }\\ \text{ Not overweight }& 10& 90\\ \text{ Overweight }& 35& 65\\ & & \end{array}$

Let $D$ be the event 'has diabetes'.
Let $N$ be the event 'not overweight'.

Determine whether having diabetes and not being overweight are independent events.

The probability that a randomly selected person has a bone disorder is $0.01$. The probability that a test for this condition is positive is $0.98$ if the condition is there, and $0.05$ if the condition is not there (a false positive).

Let $B$ be the event 'has the bone disorder' and $T$ be the event 'test is positive'.

Draw a tree diagram to represent these probabilities.

The probability that a randomly selected person has a bone disorder is $0.01$. The probability that a test for this condition is positive is $0.98$. if the condition is there, and $0.05$ if the condition is not there (a false positive).

Let $B$ be the event 'has the bone disorder' and $T$ be the event 'test is positive'.

Calculate the probability of success for the test. Note the test is successful if it tests positive for people with the disorder and negative for people without the disorder.