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Chapter 5: Q 71. (page 329)

Foreign-language study Choose a student in grades 9to 12at 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 conditional probability that a student is studying Spanish given that he or she is studying some language other than English?

Short Answer

Expert verified

Part (a) P (studying another language) =0.41

Part (b) P (Spanish another language) =0.6341

Step by step solution

01

Part (a) Step 1. Given Information 

The percentage of students who study a foreign language is shown in the table:

02

Part (a) Step 2. Concept Used 

Complement rule is P(notA)=(1鈭�P(A))

03

Part (a) Step 3. Calculation

To calculate the likelihood, use the complement rule:

P(studyinganotherlanguage)=1鈭�P(none)

P(studyinganotherlanguage)==1鈭�0.59=0.41

As a result, there is a 0.41 chance that the student is studying a language other than English.

04

Part (b) Step 3. Calculation

P (studying another language) =0.41

P(anotherlanguageandSpanish) = P(Spanish)=0.26

As a result, the required conditional probability is:

P(Spanish/anotherlanguage)=0.260.41鈮�06341

As a result, the conditional chance of a pupil studying Spanish is

P(Spanishanotherlanguage)=0.6341

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