Chapter 6.7, Problem 13E

a.

To determine

To find : the theoretical probability of landing the coin heads up.

Answer to Problem 13E

The theoretical probability of landing the coin heads up is $\frac{1}{2}$

Explanation of Solution

Given information :

A coin is tossed.

Concept used:

A theoretical probability is based on knowing all of the equally likely outcomes of an experiment.

Calculation :

In the experiment of tossing a coin, the equally likely outcomes are event of occurring heads up and tails up.

Total number of outcomes is 2.

Number of events of occurring heads up is 1.

Hence,

The theoretical probability of landing the coin heads up is obtained as:

  $\frac{\text{Number of events of occuring heads up }}{\text{total number of outcomes}}=\frac{1}{2}$

b.

To determine

To find : the experimental probability of landing heads up when the coin is tossed 20 times.

Answer to Problem 13E

The experimental probability of landing heads up when the coin is tossed 20 times is $\frac{\text{13}}{\text{20}}$ .

Explanation of Solution

Given information :

A coin is tossed 20 times.

Formula used:

An experimental probability of an event is found as:

  $P\left(\text{event}\right)=\frac{\text{Number of successes}}{\text{Number of trials}}$

Calculation :

Number of trials is 20.

On flipping the coin 20 times, number of times the coin landed heads up is 13 and number of times the coin landed tails up is 7.

So, the experimental probability of an event of landing heads up is:

  $\begin{array}{l}P\left(\text{heads up}\right)=\frac{\text{Number of successes}}{\text{Number of trials}}\\ P\left(\text{heads up}\right)=\frac{\text{13}}{\text{20}}\end{array}$

The experimental probability of landing heads up when the coin is tossed 20 times is $\frac{\text{13}}{\text{20}}$ .

c.

To determine

To compare and explain: the theoretical probability and experimental probability if a coin is tossed 100 times.

Answer to Problem 13E

If the coin is tossed 100 times, then the probability of getting heads up can be less than or more than theoretical probability that is $0.5$ .

Explanation of Solution

Given information :

A coin is tossed 100 times.

Experimental probability is calculated as $\frac{\text{13}}{\text{20}}=0.65$ while the theoretical probability is calculated as $\frac{\text{1}}{\text{2}}=0.5$ .

So, there is difference of $\left(0.65-0.5=0.15\right)$ between Experimental probability and theoretical probability although the difference is less but still if a coin is thrown once, the probability of landing heads up is $\frac{\text{1}}{\text{2}}=0.5$ .

When a coin is tossed 20 times, then the probability of getting heads up is calculated as $\frac{\text{13}}{\text{20}}=0.65$ .

Hence,

If the coin is tossed 100 times, then the probability of getting heads up can be less than or more than theoretical probability that is $0.5$ .