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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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Checkpoint 4 Worked-out solution available at LarsonAppliedCalculus.com

Three coins are tossed (see Checkpoint 3). Find the expected value of the number of heads that will turn up.

To determine

To calculate: The expected value of the number of heads that will turn up when three coins are tossed.

Explanation

Given Information:

The provided information is that the three coins are tossed.

Formula used:

Definition of Expected Value:

If the set of values of a discrete random variable consists of m different values {x1,x2,x3,,xm}, then the expected value of the random variable is

E(x)=x1P(x1)+x2P(x2)+x3P(x3)++xmP(xm).

Calculation:

Consider the provided information is that the three coins are tossed and the random variable represents the number of heads in each possible outcome.

Let, x be the random variable that represents the number of heads in each possible outcome and n(x) represent the frequency of the random variable.

The possible outcomes are shown below when three coins are tossed.

x outcome n(x)
0 TTT 1
1 HTT, THT, TTH 3
2 HHT, HTH, THH 3
3 HHH 1

The sample space S is the total possible outcome of the experiment.

So,

n(S)=23=8

Since, probability of a random variable is given as below:

P(x)=Frequency of xNumber of outcome in S=n(x)n(S)

So, the probability of each value of the random variable is shown in the table

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