Chapter 5.3, Problem 65E

(a)

To determine

Probability for the student is studying a language other than English.

Answer to Problem 65E

Probability that the student is studying a language other than English is 0.41.

Explanation of Solution

Given information:

The distribution of results:

  

According to the Complement rule,

  $P\left(\text{not}A\right)=1-P\left(A\right)$

Note that

In the table,

Probability for the students studying none of the languages other than English,

  $P\left(\text{none}\right)=0.59$

Apply complement rule:

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

Thus,

Probability for the student studying a language other than English is 0.41.

(b)

To determine

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

Answer to Problem 65E

Probability that the student is studying Spanish language other than English is approx. 0.6341.

Explanation of Solution

Given information:

The distribution of results:

  

From Part (a):

The probability of language other than English,

  $P\left(\text{other}\text{language}\right)=0.41$

According to the conditional probability,

  $P\left(\text{A}|\text{B}\right)=\frac{P\left(\text{A}\text{and}\text{B}\right)}{P\left(\text{B}\right)}$

In this case,

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

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

Apply the conditional probability:

  $P\left(\text{Spanish}|\text{other}\text{language}\right)=\frac{P\left(\text{other}\text{language}\text{and}\text{Spanish}\right)}{P\left(\text{other}\text{language}\right)}=\frac{0.26}{0.41}\approx 0.6341$

Thus,

Probability for the student studying Spanish language other than English is approx. 0.6341.