a. An elementary school is offering 3 language classes: one in Spanish, one in F

Question

a. An elementary school is offering 3 language classes: one in Spanish, one in French, and one in German. These classes are open to any of the 106 students in the school. There are 42 in the Spanish class, 38 in the French class, and 24 in the German class. There are 14 students that in both Spanish and French, 7 are in both Spanish and German, and 9 are in both French and German. In addition, there are 3 students taking all 3 classes.

i. What is the probability that exactly one of the computers will be defective?

ii. What is the probability that at least one of the computers selected is defective?

b.  A bag contains 5 red marbles, 7 white marbles, and 10 blue marbles. You draw 3 marbles out at random, without replacement. What is the probability that all the marbles are red?

i. The probability that all the marbles are red is?

ii. What is the probability that exactly two of the marbles are red?

iii. What is the probability that none of the marbles are red?

c. An elementary school is offering 3 language classes: one in Spanish, one in French, and one in German. These classes are open to any of the 106 students in the school. There are 42 in the Spanish class, 38 in the French class, and 24 in the German class. There are 14 students that in both Spanish and French, 7 are in both Spanish and German, and 9 are in both French and German. In addition, there are 3 students taking all 3 classes.

i. If one student is chosen randomly, what is the probability that he or she is taking at least one language class?

ii. If two students are chosen randomly, what is the probability that at least one of them is taking a language class?

Explanation / Answer

a) The description and question isn't matching.

b) i) P(All red) = (5/22)*(4/21)*(3/20) = 1/154

ii) P(Exactly two red) = 3*(5/22)*(4/21)*(17/20) = 17/154

iii) P(None red) = (17/22)*(16/21)*(15/20) = 34/77

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