Chapter 5: Q 71. (page 329)

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?

Expert verified

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

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

Step by step solution

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

Complement rule is $P (n o t A) = (1 - P (A))$

To calculate the likelihood, use the complement rule:

$P (s t u d y i n g a n o t h e r l a n g u a g e) = 1 - P (n o n e)$

$P (s t u d y i n g a n o t h e r l a n g u a g e) = = 1 - 0.59 = 0.41$

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

P (studying another language) = $0.41$

$P (a n o t h e r l a n g u a g e a n d S p a n i s h)$ = $P (S p a n i s h) = 0.26$

As a result, the required conditional probability is:

$P (S p a n i s h / a n o t h e r l a n g u a g e) = \frac{0.26}{0.41} \approx 06341$

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

$P (S p a n i s h a n o t h e r l a n g u a g e) = 0.6341$

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