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Chapter 4: Problem 44

What is meant by the joint probability of two or more events? Give one example.

Short Answer

Expert verified
Joint probability is the statistical measure that calculates the likelihood of two events happening simultaneously. For instance, if a fair six-sided die is rolled, the joint probability of the die landing on an even number (Event A) and a number less than 5 (Event B), P(A 鈭� B), is \(\frac{2}{6}\) or approximately 0.33.

Step by step solution

01

Define Joint Probability

The first step to answering this exercise is to define joint probability. Joint probability is a statistical measure that calculates the likelihood of two events happening at the same time.
02

Elaborate on Joint Probability

To elaborate further, if we have two events A and B, the joint probability of A and B (usually denoted as P(A and B) or P(A 鈭� B)) is the probability that both A and B occur.
03

Provide an Example

An example can help to understand this concept more concretely. Suppose we have a fair six-sided die. Event A is the die landing on an even number, and Event B is the die landing on a number less than 5. The probability of these two events happening at the same time would be the joint probability of A and B.
04

Calculate Joint Probability using the Example

In terms of calculation, there are three even numbers (2, 4, 6) and four numbers less than 5 (1, 2, 3, 4) on a six-sided die. The numbers that satisfy both conditions are 2 and 4, which makes 2 numbers out of 6. Therefore, the joint probability P(A 鈭� B) can be calculated as \(\frac{2}{6}\) or approximately 0.33.

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Most popular questions from this chapter

There is an area of free (but illegal) parking near an inner-city sports arena. The probability that a car parked in this area will be ticketed by police is . 35 , that the car will be vandalized is \(.15\), and that it will be ticketed and vandalized is . 10 . Find the probability that a car parked in this area will be ticketed or vandalized.

A die is rolled once. What is the probability that a. a number less than 5 is obtained? b. a number 3 to 6 is obtained?

Given that \(P(B \mid A)=.70\) and \(P(A\) and \(B)=.35\), find \(P(A)\).

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A restaurant menu has four kinds of soups, eight kinds of main courses, five kinds of desserts, and six kinds of drinks. If a customer randomly selects one item from each of these four categories, how many different outcomes are possible?
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