Chapter 15.10, Problem 5OE

(a)

To determine

To find:Theevent in each problem is the dependent or independentevents.

Answer to Problem 5OE

The twoevents are independent.

Explanation of Solution

Given information:

The given information is

  $pink=3$

  $green=3$

  $totaleraser=6$ .

Calculation:

Independent Event: - When the outcome of one event doesn’t affect the outcome of others.

  $P\left(A\cap B\right)=P\left(A\right)\times P\left(B\right)$

Dependent Event: - When the outcomes of one event affect the outcome of others.

  $P\left(A\cap B\right)=P\left(A\right)\times P\left(B|A\right)$

  $\begin{array}{l}P\left(pink\right)=\frac{3}{6}=\frac{1}{2}\\ P\left(green\right)=\frac{3}{6}=\frac{1}{2}\end{array}$

Probability that both erasers are green $=\frac{1}{2}\times \frac{1}{2}=\frac{1}{4}$

Theoutcome of one event doesn’t affect the outcome of others, so the twoevents independent.

Thus,the twoevents are independent.

(b)

To determine

To find:The event in each problem is the dependent or independentevents.

Answer to Problem 5OE

The $A$ and $B$ are independent.

Explanation of Solution

Given information:

The given information is

Two light bulb of $60$ watt

Two light bulb of $75$ watt.

Calculation:

Independent Event: - When the outcome of one event doesn’t affect the outcome of others.

  $P\left(A\cap B\right)=P\left(A\right)\times P\left(B\right)$

Dependent Event: - When the outcomes of one event affect the outcome of others.

  $P\left(A\cap B\right)=P\left(A\right)\times P\left(B|A\right)$

The Probability of choosing one $75$ watts light bulb is $=\frac{2}{4}=\frac{1}{2}$

Then after this there are three light bulbs remaining,

The probability of choosing a $60$ watt light bulb is $=\frac{2}{3}$ .

Thus the probability of choosing a watts then a watt bulb is denoted by $=\frac{2}{4}\times \frac{2}{3}=\frac{1}{3}$

The two events are dependent as the outcomes of one event affect the outcome of others.

Thus,the two events are dependent.