Chapter 13.3, Problem 24AYU

In Problems 23-26, consider the experiment of tossing a coin twice. The table lists six possible assignments of probabilities for this experiment. Using this table, answer the following questions.

Which of the assignments of probabilities should be used if the coin is known to be fair?

To determine

Which of the assignments of probabilities should be used if the coin is known to be fair?

Answer to Problem 24AYU

A

Explanation of Solution

Given:

Consider the experiment of tossing a coin twice. The table lists six possible assignments of probabilities for this experiment.

Formula used:

Probability of any event is $0\le P\left(E\right)\le 1$.

${\displaystyle \sum }_{i=1}^{n}P\left(e_i\right)=P\left(e_1\right)+P\left(e_2\right)+\cdot \cdot \cdot +P\left(e_n\right)=1$

Calculation:

Since the coin is fair, the four outcomes $\left(HH,HT,TH,TT\right)$ are equally likely, therefore, the probability of each of the four outcomes is $1/4$. Hence assignment A represents assignment where a fair coin is used.