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’s 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?

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 is $0.6341 .$

Step by step solution

It is given that:

As per complement rule: $P (not A) = 1 - P (A)$

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 is $0.41$

From above part: $P (other language) = 0.41$

We know that $P (A ∣ B) = \frac{P (A and B)}{P (B)}$

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

$P (Spanish ∣ other language) = \frac{P (otherlanguageandSpanish)}{P (otherlanguage)} = \frac{0.26}{0.41} \approx 0.6341$

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