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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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