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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 economist says that the probability is \(.47\) that a randomly selected adult is in favor of keeping the Social Security system as it is, \(.32\) that this adult is in favor of totally abolishing the Social Security system, and .21 that this adult does not have any opinion or is in favor of other options. Were these probabilities obtained using the classical approach, relative frequency approach, or the subjective probability approach? Explain your answer.

Define the following terms: experiment, outcome, sample space, simple event, and compound event.

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.

A thief has stolen Roger's automatic teller machine (ATM) card. The card has a four-digit personal identification number (PIN). The thief knows that the first two digits are 3 and 5 , but he does not know the last two digits. Thus, the PIN could be any number from 3500 to \(3599 .\) To protect the customer, the automatic teller machine will not allow more than three unsuccessful attempts to enter the PIN. After the third wrong PIN, the machine keeps the card and allows no further attempts. a. What is the probability that the thief will find the correct PIN within three tries? (Assume that the thief will not try the same wrong PIN twice.) b. If the thief knew that the first two digits were 3 and 5 and that the third digit was either 1 or 7 , what is the probability of the thief guessing the correct PIN in three attempts?

What is the joint probability of two mutually exclusive events? Give one example.
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