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Chapter 13: Q. 28 (page 865)

Assigning Probabilities A coin is weighted so that tails is twice as likely as heads to occur. What probability should we assign to heads? to tails?

Short Answer

Expert verified

The probability is $P (T) = \frac{2}{3}, P (H) = \frac{1}{3}$ .

Step by step solution

01

Step 1. Given information.

A coin is weighted so that tails is twice as likely as heads to occur. What probability should we assign to heads? to tails?

02

Step 2. Find probability.

We are given that the tail Tis twice times as likely as heads Hto occur in a coin. Thus, we can let

$P (H) = x P (T) = 2 x$

Since the sum of the probabilities of the possible outcomes must equal 1, we have

$P (T) + P (H) = 1$

Substituting the value of localid="1647255351165" $P (T) and P (H)$ and solving for x ,we have

$P (T) + P (H) = 1 2 x + x = 1 3 x = 1 x = \frac{1}{3}$

Since $x = \frac{1}{3}$ , assign the probabilities

$P (T) = 2 x = \frac{2}{3}, P (H) = x = \frac{1}{3}$ .

03

Step 3. Conclusion.

The probability is $P (T) = \frac{2}{3}, P (H) = \frac{1}{3}$ .

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Most popular questions from this chapter

List all the ordered arrangements of 5 objects $a, b, c, d$ , and $e$ choosing 2 at a time without repetition. What is $P (5, 2)$ ?

$P (n, r) =______$

In Problems 11–16, construct a probability model for each experiment.

Tossing three fair coins once.

Use the formula $C (n, r) = \frac{n!}{(n - r)! r!}$ to find the value of each combination.

$C (8, 2)$

A golf ball is selected at random from a container. If the container has 9 white balls, 8 green balls, and 3 orange balls, find the probability of each event.

The golf ball is white or orange.

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