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Chapter 5: Q 65. (page 332)

Foreign-language studyChoose a student in grades 9 to 12 at random and ask if he or she is studying a language other than English. Here is the distribution of results:

a. What鈥檚 the probability that the student is studying a language other than English?

b. What is the probability that a student is studying Spanish given that he or she is

studying some language other than English?

Short Answer

Expert verified

a. Probability for students is studying a language other than English is 0.41.

b. Probability that student is studying Spanish other than English is0.6341.

Step by step solution

01

Given Information

It is given that:

02

Probability for student is studying language other than English

As per complement rule: P(notA)=1-P(A)

From table:

Probability that student is studying none language other than English is P(none)=0.59

From complement rule,

P(other language)=1-P(none)=1-0.59=0.41

Probability that student is studying language other than English is0.41

03

Probability for the student studying some language other than English is Spanish.

From above part: P(other language)=0.41

We know that P(A鈭�B)=P(AandB)P(B)

Here, the probability of other language and Spanish language will be same as probability of Spanish language.

P(other language and Spanish)=P(Spanish)=0.26

As per conditional probability

P(Spanish鈭�other language)=P(otherlanguageandSpanish)P(otherlanguage)=0.260.41鈮�0.6341

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Most popular questions from this chapter

Middle school values Researchers carried out a survey of fourth-, fifth-, and sixth-grade students in Michigan. Students were asked whether good grades, athletic ability, or being popular was most important to them. The two-way table summarizes the survey data.

Suppose we select one of these students at random.

  1. Find P(athletic | 5thgrade).
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Is this your card? A standard deck of playing cards (with jokers removed) consists of 52 cards in four suits鈥攃lubs, diamonds, hearts, and spades. Each suit has 13 cards, with denominations ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, jack, queen, and king. The jacks, queens, and kings are referred to as 鈥渇ace cards.鈥� Imagine that we shuffle the deck thoroughly and deal one card. The two-way table summarizes the sample space for this chance process based on whether or not the card is a face card and whether or not the card is a heart.

Type of card

Face cardNon-Face cardTotal
Heart3
10
13
Non-Heart9
30
39
Total12
40
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Are the events 鈥渉eart鈥� and 鈥渇ace card鈥� independent? Justify your answer.

Teachers and college degrees Select an adult at random. Define events D: person has earned a college degree, and T: person鈥檚 career is teaching. Rank the following probabilities from smallest to largest. Justify your answer.

P(D)P(T)P(DT)P(TD)

Free-throw practice At the end of basketball practice, each player on the team must shoot free throws until he makes 10of them. Dwayne is a 70%free-throw shooter. That is, his probability of making any free throw is 0.70. We want to design a simulation to estimate the probability that Dwayne make10 free throws in at most 12shots. Describe how you would use each of the following chance devices to perform one trial of the simulation.

a. Slips of paper

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Who eats breakfast?Students in an urban school were curious about how many children regularly eat breakfast. They conducted a survey, asking, 鈥淒o you eat breakfast on a regular basis?鈥� All 595students in the school responded to the survey. The resulting data are shown in the two-way table.

Suppose we select a student from the school at random. Define event Fas getting a female student and event Bas getting a student who eats breakfast regularly.

a. Find P(BC)

b. Find P(FandBC). Interpret this value in context.

c. Find P(ForBC).
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