Question

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?

Short answer

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

Given Information

It is given that:

Probability for student is studying language other than English

As per complement rule: $P(notA)=1-P\left(A\right)$

From table:

Probability that student is studying none language other than English is $P\left(\text{none}\right)=0.59$

From complement rule,

$P\left(\text{other language}\right)=1-P\left(\text{none}\right)=1-0.59=0.41$

Probability that student is studying language other than English is$0.41$

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

From above part: $P\left(\text{other language}\right)=0.41$

We know that $P(\mathrm{A}\mid \mathrm{B})=\frac{P(\mathrm{A}\text{and}\mathrm{B})}{P(\mathrm{B})}$

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

$P\left(\text{other language and Spanish}\right)=P\left(\text{Spanish}\right)=0.26$

As per conditional probability

$P(\text{Spanish}\mid \text{other language})=\frac{P\left(\text{otherlanguageandSpanish}\right)}{P\left(\text{otherlanguage}\right)}=\frac{0.26}{0.41}\approx 0.6341$