Bilingual and Trilingual. At a certain university in the United States, 62 % of the students are at least bilingual - speaking English and at least one other language. Of these students, 80 % speak Spanish and, of the 80 % who speak Spanish, 10 % also speak French. Determine the probability that a randomly selected student at this university

(a) does not speak Spanish.

(b) speaks Spanish and French.

The given statement is:

At a certain university in the United States, 62 % of the students are at least bilingual - speaking English and at least one other language.

Of these students, 80 % speak Spanish and, of the 80 % who speak Spanish, 10 % also speak French.

Let's assume that the total number of pupils is x.

As a result, the number of students who speak Spanish will become:

$0.8x$.

Therefore, the number of students who do not speak Spanish will become:

$x-0.8x=0.2x$

The probability that a student is chosen at random who does not speak Spanish is:

$$\begin{gathered} P\left(E\right)=\frac{0.2x}{x} \\ =0.2 \end{gathered}$$

It is given that the 80 % who speak Spanish, 10 % of them also speak French.

Therefore, the number of students who speak both Spanish and French is:

$$\begin{gathered} 0.8x\times \frac{10}{100} \\ =0.08x \end{gathered}$$

The probability that a student is chosen at random who speaks Spanish and French is:

$$\begin{gathered} P\left(E\right)=\frac{0.08x}{x} \\ =0.08 \end{gathered}$$