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Chapter 4: Problem 67

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

Short Answer

Expert verified
Joint probability is the likelihood of two events occurring simultaneously. For example, the joint probability of rolling a 3 on the first die and a 4 on the second die, when rolling two dice, is \( \frac{1}{36} \) or approximately 0.0278.

Step by step solution

01

Defining Joint Probability

Joint probability is the statistical term indicating the likelihood of two events occurring simultaneously. In simpler terms, it measures the probability of both event A and event B occurring at the same time.
02

Example of Joint Probability

For example, consider the rolling of two dice. Each die has six faces, each face equating to an outcome. The total possible outcomes when rolling two dice is \(6 \times 6 = 36\). If we want to find the joint probability of rolling a 3 on the first die (event A) and a 4 on the second die (event B), we need to realize that there is only one outcome that satisfies both A and B, which is rolling a 3 on the first die and a 4 on the second. So, the joint probability is \( \frac{1}{36} \), or approximately 0.0278.

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Most popular questions from this chapter

According to a survey of 2000 home owners, 800 of them own homes with three bedrooms, and 600 of them own homes with four bedrooms. If one home owner is selected at random from these 2000 home owners, find the probability that this home owner owns a house that has three or four bedrooms. Explain why this probability is not equal to \(1.0 .\)

Given that \(P(A \mid B)=.40\) and \(P(A\) and \(B)=.36\), find \(P(B)\).

A trimotor plane has three engines-a central engine and an engine on each wing. The plane will crash only if the central engine fails and at least one of the two wing engines fails. The probability of failure during any given flight is \(.005\) for the central engine and \(.008\) for each of the wing engines. Assuming that the three engines operate independently, what is the probability that the plane will crash during a flight?

The probability of a student getting an A grade in an economics class is \(.24\) and that of getting a B grade is \(.28\). What is the probability that a randomly selected student from this class will get an \(\mathrm{A}\) or a \(\mathrm{B}\) in this class? Explain why this probability is not equal to \(1.0\)

The following table gives a two-way classification of all basketball players at a state university who began their college careers between 2001 and 2005, based on gender and whether or not they graduated. $$\begin{array}{lcc} \hline & \text { Graduated } & \text { Did Not Graduate } \\ \hline \text { Male } & 126 & 55 \\ \text { Female } & 133 & 32 \\ \hline \end{array}$$ If one of these players is selected at random, find the following probabilities. a. \(P(\) female or did not graduate) b. \(P(\) graduated or male \()\)
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