Chapter 12.5, Problem 9PPS

To determine

To state whether the events are independent or dependent find the probability of getting tails all four times.

Answer to Problem 9PPS

The event is independent and the probability of getting a tails all four times is $\frac{1}{16}\text{ or 6}\text{.25\%}$ .

Explanation of Solution

Given information:

The given statement is:

“If a coin in tossed $4$ times, what is the probability of getting tails all $4$ times?”

Formula used:

The following formula is used:

  $\text{Probability}=\frac{\text{Number of possible outcomes}}{\text{Total number of outcomes}}$

Calculation :

The result of one toss does not affect the result of another, so it is an independent event.

The probability of getting tails can be calculated by:

  $\begin{array}{l}\text{P}\left(\text{tails}\right)=\frac{1}{2}\\ \text{P}\left(\text{tails, tails, tails, tails}\right)=\frac{1}{2}\times \frac{1}{2}\times \frac{1}{2}\times \frac{1}{2}\\ \text{P}\left(\text{tails, tails, tails, tails}\right)=\frac{1}{16}\text{ or 6}\text{.25\%}\end{array}$

Hence, the event is independent and the probability of getting a tails all four times is $\frac{1}{16}\text{ or 6}\text{.25\%}$ .