Question

Qe 190 stodents, 20 can speak fiench, 14 can speak German; and 8 can speak beth French and German. If a student is picked at random, what is the probabaty that he ar she ean abeak French is Genimin?

Answer 1

To determine the probability that a randomly picked student among 190 students can speak either French or German, use the principle of inclusion-exclusion, which yields a probability of 13.68%.

Step-by-step explanation:

The question pertains to calculating the probability that a randomly selected student can speak French or German. Among the 190 students, 20 can speak French, 14 can speak German, and 8 can speak both French and German. To find the probability that the student picked at random can speak either of the languages, we can use the principle of inclusion-exclusion.

The formula for the probability of A or B is P(A) + P(B) - P(A and B), where A is the event of speaking French, and B is the event of speaking German. So, the probability that a student speaks French or German is:

P(French or German) = P(French) + P(German) - P(French and German).

Substituting the values we have:

P(French or German) = (20/190) + (14/190) - (8/190) = (26/190) = 13.68%.