Chapter 20, Problem 7E

(a)

To determine

To explain do two losses in a row convince you that he really can control the toss.

Answer to Problem 7E

No, it does not.

Explanation of Solution

It is given in the question that a friend of yours claims that when he tosses a coin he can control the outcome. He tosses a coin and it is head and you losses. Thus, the two losses in a row do not convince us that he really can control the toss because there is a $25\%$ chance of losing two times in a row and that does not seem unusual.

(b)

To determine

To find out what is the probability of losing three tosses in a row if the process is fair.

Answer to Problem 7E

  $0.125$ .

Explanation of Solution

It is given in the question that a friend of yours claims that when he tosses a coin he can control the outcome. He tosses a coin and it is head and you losses. Thus, the probability of losing three tosses in a row if the process is fair can be calculated as:

  $\begin{array}{l}0.5\times 0.5\times 0.5\\ =0.125\end{array}$

(c)

To determine

To explain would three losses in a row convince you that your friend cheats.

Answer to Problem 7E

No, we would not be.

Explanation of Solution

It is given in the question that a friend of yours claims that when he tosses a coin he can control the outcome. He tosses a coin and it is head and you losses. Thus, we can say that if there isthree losses in a row we would not be convincedthat our friend cheats because there is a $0.125$ chance it will happen as we know $\text{1 out of 8}$ times it will happen.

(d)

To determine

To explain how many times in a row would you have to lose in order to be pretty sure that this friend really can control the toss.

Answer to Problem 7E

We need five times in a row.

Explanation of Solution

It is given in the question that a friend of yours claims that when he tosses a coin he can control the outcome. He tosses a coin and it is head and you losses. Thus, to find out how many times in a row would you have to lose in order to be pretty sure that this friend really can control the toss, then we can say five times because the probability for five losses is $0.03125$ , which means we will only win once out of $32$ tries and it seems unusual.