Question

According to the “Book of Odds,” the probability that a randomly selected U.S. adult usually eats breakfast is $0.61$

(a) Explain what probability $0.61$ means in this setting.

(b) Why doesn’t this probability say that if $100$ U.S. adults are chosen at random, exactly $61$of them usually eat breakfast?

Short answer

Part (a) A large sample of U.S. adults about $61\%$eat breakfast.

Part (b) A randomly selected U.S. adult usually eats breakfast is$0.61$

Step-by-step solution

Part (a) Step 1. Given Information

Breakfast is normally eaten by$0.61$of a randomly picked adult in the United States.

Part (a) Step 2. Concept

The ratio of two positive integers with no common factor is known as odds. If A is the outcome of a sample space, then the odds are in A's favors.

Part (a) Step 3. Calculation

If A is the outcome of a sample space, then the odds are in A's favor.

$=\frac{P\left(A\right)}{P\left(A^c\right)}$

That is $P\left(A\right):P(A^c)$

In this case, the chances likelihood of $0.61$means

That is $=\frac{0.61\times 100\times 100}{100}$

$=61\%$

This means that a large sample of U.S. adult about $61\%$ eat breakfast

Part (b) Step 1. Calculation

If A is the outcome of a sample space, then the odds are in A's favor.

$=\frac{P\left(A\right)}{P\left(A^c\right)}$

That is $P\left(A\right):P\left(A^c\right)$

The books of odds probability $0.61$ means in this setting

That is $=\frac{0.61\times 100\times 100}{100}$

$=61\%$

Although it this expect around $61$adults will eat breakfast the exact number will differ from sample to sample.