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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

An automated teller machine at a local bank is stocked with \(\$ 10\) and \(\$ 20\) bills. When a customer withdraws \(\$ 40\) from the machine, it dispenses either two \(\$ 20\) bills or four \(\$ 10\) bills. If two customers withdraw \(\$ 40\) each, how many outcomes are possible? Draw a tree diagram for this experiment.

How is the addition rule of probability for two mutually exclusive events different from the rule for two events that are not mutually exclusive?

List the simple events for each of the following statistical experiments in a sample space. a. One roll of a die b. Three tosses of a coin c. One toss of a coin and one roll of a die

In a large city, 15,000 workers lost their jobs last year. Of them, 7400 lost their jobs because their companies closed down or moved, 4600 lost their jobs due to insufficient work, and the remainder lost their jobs because their positions were abolished. If one of these 15,000 workers is selected at random, find the probability that this worker lost his or her job a. because the company closed down or moved b. due to insufficient work c. because the position was abolished Do these probabilities add to \(1.0 ?\) If so, why?

Define the following two events for two tosses of a coin: \(A=\) at least one head is obtained \(B=\) two tails are obtained a. Are \(A\) and \(B\) mutually exclusive events? Are they independent? Explain why or why not. b. Are \(A\) and \(B\) complementary events? If yes, first calculate the probability of \(B\) and then calculate the probability of \(A\) using the complementary event rule.
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