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Chapter 4: Problem 29

Briefly explain the difference between the marginal and conditional probabilities of events. Give one example of each.

Short Answer

Expert verified
Marginal probability is the chance of a specific event occurring, irrespective of any other events, e.g., rolling a 3 on a dice has a probability of 1/6. Conditional probability, conversely, is the chance of an event happening given that another event has already occurred, e.g., the probability of drawing a King given a Heart from a deck of cards is 1/13. The main distinction is that marginal probability is about the occurrence of single events, while conditional probability considers that another event has already taken place.

Step by step solution

01

Understanding and Explaining Marginal Probability

Marginal Probability refers to the chance of one specific event happening, irrespective of any other events. A simple demonstration of this could be the roll of a single dice where each outcome (getting a 1, 2, 3, 4, 5, or 6) is independent of any other. Let鈥檚 say event A is getting a 3, then the marginal probability of A, denoted as P(A), would be 1/6 since there鈥檚 one '3' in a dice of six faces.
02

Understanding and Explaining Conditional Probability

Conditional Probability, on the other hand, refers to the chance of an event happening given that another event has already happened. For instance, consider a deck of cards, and let Event A be drawing a King from it, and Event B be the card drawn is a Heart. The conditional probability of drawing a King given that we've drawn a Heart, denoted as P(A|B), would be 1/13 since there鈥檚 only one King in the 13 Hearts.
03

Distinction between Marginal and Conditional Probability

The key difference between marginal and conditional probability lies in their dependence on other events. Marginal probability is concerned with the probability of a single event happening in isolation, while Conditional probability takes into account that another event has already occurred.

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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.

Recent uncertain economic conditions have forced many people to change their spending habits. In a recent telephone poll of 1000 adults, 629 stated that they were cutting back on their daily spending. Suppose that 322 of the 629 people who stated that they were cutting back on their daily spending said that they were cutting back somewhat and 97 stated that they were cutting back somewhat and delaying the purchase of a new car by at least 6 months. If one of the 629 people who are cutting back on their spending is selected at random, what is the probability that he/she is delaying the purchase of a new car by at least 6 months given that he/she is cutting back on spending somewhat?

The probability that a student graduating from Suburban State University has student loans to pay off after graduation is .60. If two students are randomly selected from this university, what is the probability that neither of them has student loans to pay off after graduation?

How many different outcomes are possible for four rolls of a die?

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