Question

Foreign-language study Choose 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 conditional probability that a student is studying Spanish given that he or she is studying some language other than English?

Short answer

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

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

Step-by-step solution

Part (a) Step 1. Given Information 

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

Part (a) Step 2. Concept Used 

Complement rule is $P(notA)=(1-P(A\left)\right)$

Part (a) Step 3. Calculation

To calculate the likelihood, use the complement rule:

$P(studyinganotherlanguage)=1-P\left(none\right)$

$P(studyinganotherlanguage)==1-0.59=0.41$

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

Part (b) Step 3. Calculation

P (studying another language) =$0.41$

$P(anotherlanguageandSpanish)$ = $P\left(Spanish\right)=0.26$

As a result, the required conditional probability is:

$P(Spanish/anotherlanguage)=\frac{0.26}{0.41}\approx 06341$

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

$P(Spanishanotherlanguage)=0.6341$