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Chapter 4: Problem 3

Notation When selecting one of your Facebook Friends, let event \(F=\) female and let event \(H=\) high school classmate. Use your own words to translate the notation \(P(H | F)\) into a verbal statement.

Short Answer

Expert verified
The probability that a Facebook friend is a high school classmate, given that the friend is female.

Step by step solution

01

Identify Known Elements

Determine what each notation represents. Here, event F denotes 'female', and event H denotes 'high school classmate'.
02

Understand Conditional Probability Notation

The notation P(H | F) represents the conditional probability that event H occurs given that event F has already occurred.
03

Translate into Words

Combine the identified elements and the understanding of conditional probability. Translate P(H | F) as 'The probability that a Facebook friend is a high school classmate, given that the friend is female.'

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

probability notation
Probability notation helps us to express complex concepts in a simple and understandable format. It uses symbols to represent the likelihood of different events. For example, in the exercise, we see the notation P(H | F). Here, 'P' stands for probability, 'H' represents the event of being a high school classmate, and 'F' represents the event of being female. The '|' symbol means 'given that' or 'conditional on'. Therefore, P(H | F) reads as the probability that a friend is a high school classmate, given that the friend is female.
conditional probability
Conditional probability is a fundamental concept in probability theory. It refers to the probability of an event occurring given that another event has already occurred. In our exercise, we are looking at P(H | F). This represents the probability that a friend is a high school classmate (H) given that we know the friend is female (F). Conditional probability can be expressed mathematically using the formula: \[ P(A | B) = \frac{P(A \cap B)}{P(B)} \]This means that the conditional probability of event A given event B is the probability of both events occurring divided by the probability of event B.
events in probability
In probability, an event is a set of outcomes to which we assign a probability. Events can be simple or compound. Simple events have only one outcome, like drawing a red card from a deck of cards. Compound events combine two or more simple events, like drawing a red card and then a black card. In the exercise, event F (female) and event H (high school classmate) are being considered. These events can have different intersections, unions, and conditional dependencies, which is what makes probability a versatile and powerful field of mathematics.

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Most popular questions from this chapter

Find the probability.At Least One. In Exercises \(5-12,\) find the probability. Assuming that boys and girls are equally likely, find the probability of a couple having a boy when their third child is born, given that the first two children were both girls.

Express all probabilities as fractions. Mendel conducted some his famous experiments with peas that were either smooth yellow plants or wrinkly green plants. If four peas are randomly selected from a batch consisting of four smooth yellow plants and four wrinkly green plants, find the probability that the four selected peas are of the same type.

Express the indicated degree of likelihood as a probability value between \(\boldsymbol{0}\) and \(\boldsymbol{I}\).When using a computer to randomly generate the last digit of a phone number to be called for a survey, there is 1 chance in 10 that the last digit is zero.

Use the given probability value to determine whether the sample results could easily occur by chance, then form a conclusion.A study addressed the issue of whether pregnant women can correctly predict the gender of their baby. Among 104 pregnant women, 57 correctly predicted the gender of their baby (based on data from "Are Women Carrying 'Basketballs'. by Perry, DiPietro, Constigan, Birth, Vol. 26, No. 3). If pregnant women have no such ability, there is a 0.327 probability of getting such sample results by chance. What do you conclude?

Probability of At Least One Let \(A=\) the event of getting at least 1 defective iPhone when 3 iPhones are randomly selected with replacement from a batch. If \(5 \%\) of the iPhones in a batch are defective and the other \(95 \%\) are all good, which of the following are correct? a. \(P(\bar{A})=(0.95)(0.95)(0.95)=0.857\) b. \(P(A)=1-(0.95)(0.95)(0.95)=0.143\) c. \(P(A)=(0.05)(0.05)(0.05)=0.000125\)
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