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Chapter 3: Q. 37 (page 217)

What is the sum of the probabilities of an event and its complement?

Short Answer

Expert verified

The sum of an event's probability and its complement is1.

Step by step solution

01

Introduction

The term "probability" simply refers to the likelihood of something occurring. We may talk about the probabilities of particular outcomes—how likely they are—when we're unclear about the result of an event. Statistics is the study of occurrences guided by probability.
02

Explanation

The sum of an event and its complement is always equal to 1.

Complement of event "A" is "not Anwhich is denoted by A*.

Let us consider it with the example. Let us consider that for a coin, if the result is head then the complement will be tail. So as per the rule, the sum of the probabilities should be coming to one.

Hence, we can write as : P(A)+PA'=1

Here,

P(A)=probability of the coin, coming to head.

PA'=probability of the coin, coming to tail.

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Most popular questions from this chapter

Let event A = learning Spanish. Let event B = learning German. Then A AND B = learning Spanish and German.Suppose P(A) = 0.4 and P(B) = 0.2. P(A AND B) = 0.08. Are events A and B independent? Hint: You must show ONE of the following:

• P(A|B) = P(A)

• P(B|A) = P(B)

• P(A AND B) = P(A)P(B)

In words, explain what it means to pick one person from the study who is “Japanese American GIVEN that person smokes 21to30 cigarettes per day.” Also, find the probability

A box is filled with several party favors. It contains 12

hats, 15 noisemakers, ten finger traps, and five bags of confetti.

Let H = the event of getting a hat.

Let N = the event of getting a noisemaker.

Let F = the event of getting a finger trap.

Let C = the event of getting a bag of confetti.

Find P(N).

Use the following information to answer the next 12exercises. The graph shown is based on more than localid="1648902668215">170,000interviews done by Gallup that took place from January through December 2012. The sample consists of employed Americans 18years of age or older. The Emotional Health Index Scores are the sample space. We randomly sample one Emotional Health Index Score.

If we know an Emotional Health Index Score is 81.5 or more, what is the probability that it is 82.7.

A student goes to the library. Let events B = the student checks out a book and D = the student checks out a DVD. Suppose that P(B) = 0.40, P(D) = 0.30 and P(B AND D) = 0.20.

a. Find P(B|D).

b. Find P(D|B).

c. Are B and D independent?

d. Are B and D mutually exclusive?
See all solutions

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