1. Consider the student population in a college campus. Assume that 55% of the s

Question

1. Consider the student population in a college campus. Assume that 55% of the
students are female. Assume that 20% of the male drink and 10% of the female
drink.
(a) Pick a female student at random, what is the probability that she does not drink?
(b) Pick a student at random, what is the probability that the student does not drink?
(c) Pick a student at random, what is the probability that this student is male and
drinks?
2. A company has two factories A and B. Assume that factory A produces 80% of
the products and B the remaining 20%. The proportion of defectives are 0.05 for A
and 0.01 for B.
(a) What is the probability that a product picked at random comes from A and is
not defective?
(b) What is the probability that a product picked at random is defective?
3. Consider two boxes labeled 1 and 2. In box 1 there are two black balls and three
white balls. In box 2 there are three black balls and two white balls. We pick box 1
with probability 1/3 and box 2 with probability 2/3. Then we draw a ball in the box
we picked.
(a) Given that we pick box 2 what is the probability of drawing a white ball?
(b) Given that we draw a white ball what is the probability that we picked box 1?
(c) What is the probability of picking a black ball?
4. Consider an electronic circuit with components C1 and C2. The probability that
C1 fails is 0.1. If C1 fails the probability that C2 fails is 0.15. If C1 works the
probability that C2 fails is 0.05.
(a) What is the probability that both components fail?
(b) What is the probability that at least one component works?
(c) What is the probability that C2 works?

Explanation / Answer

1) SOlving the first question

(a) Pick a female student at random, what is the probability that she does not drink? - Probability =1- 10%=0.9

(b) Pick a student at random, what is the probability that the student does not drink? Probailbity = 0.45*0.80+0.55*0.9=0.855

c) P( male and drinks ) = 45%* 20%=0.09

Please post the other questions individually.

c)

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