n elementary school is offering 3 language classes: one in Spanish, one in Frenc

Question

n elementary school is offering 3 language classes: one in Spanish, one in French, and one in German. There are 28% students in the Spanish class, 26% in the French class and 16% in the German class. There are 12% students that are in both Spanish and French, 490 that are in both Spanish and German, and 600 that are in both French and German. In addition, there are 2% students taking all 3 classes. a. If a student is chosen randomly, what is the probability that he or she is not in any of the language class? Sol b. If a student is chosen randomly, what is the probability that he or she is taking either French or German? Sol If a student is chosen randomly, what is the probability that he or she is taking Spanish but not German? Sol d. What is the conditional probability that a randomly selected student is taking a French class given that he or she is taking a Spanish class'? Sol

Explanation / Answer

a) Probability = 1 - P(S U F U G)

= 1 - (0.28 + 0.26 + 0.16 - 0.12 - 0.04 - 0.06 + 0.02)

   = 1 - 0.5 = 0.5

b) P(F or G) = P(F) + P(G) - P(F and G)

                    = 0.26 + 0.16 - 0.06

                    = 0.36

c) P(S but not G) = 0.28 - 0.04 - 0.02 = 0.22

d) P(F|S) = P(F and S)/P(S)

               = 0.12/0.28 = 0.43

             

Related Questions

Navigate

• Browse (All)
• Browse N
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.