Multiple choice question from Probability and Set Language.

Choose the one alternative that best completes the statement or answer the question.
1.Which of the following events are mutually exclusive?
a.being a steelworker and being a stamp collector
b.being a college student and being a high school graduate
c.Living in Baltimore and working in Washington, D.C.
d.being a mother and being un uncle
e.none of the above

2.Two events A and B are mutually exclusive if
a.A ∩ B=Ø.
b.A ∩ B=U.
c.A υ B=U.
d.A υ B= Ø .
e.none of the above

A light bulb manufacturer tests a light bulb by letting it burn until it burns out. The experiment consists of observing how long (in hours) the light bulb burns. Let E be the event "the bulb lasts less than 100 hours," F be the event "the bulb lasts less than 50 hours," and G be the event "the bulb lasts more than 120 hour."
3. The event E υ F is
a."The bulb lasts less than 100 hours".
b."The bulb lasts between 50 and 100 hours".
c."The bulb lasts more than 50 hours".
d"The bulb lasts less than 50 hours".
e.None of the above

4.The event F' ∩ G' is
a.All possible times.
b."The bulb lasts between 120 hours or less".
c."The bulb lasts 50 hours or more".
d."The bulb lasts between 50 and 120 hours inclusive".
e.None of the above

5.Which of  the following is a valid probability distribution for a sample space S = {a, b, c, d}?
a.Pr(a) = 0.3, Pr(b) = 0.1, Pr(c) = 0.2, Pr(d) = 0.5
b.Pr(a) = 0.2, Pr(b) = 0.5, Pr(c) = 0.4, Pr(d) = 0.3
c.Pr(a) = 0.6, Pr(b) = 0, Pr(c) = 0.3, Pr(d) = 0.1
d.Pr(a) = 0.5, Pr(b) = 0.2, Pr(c) = 0.1, Pr(d) = 0.3
e.none of the above

6.Two fair die are rolled. The probability that the numbers that appear add to 4 is
a.1/36
b.1/5
c.1/6
d.1/12
e.none of the above

7. If the odds against an event are 2 to 5, then the probability that the event will occur is
a.3/5
b.2/5
c.2/7
d.3/7
e.none of the above

8.A fair coin is tossed six times. The probability of obtaining no heads is
a.1/32.
b.0/64=0.
c.1/64
d.6/64=3/32
e.none of the above

9.A fair coin is tossed six times. The probability of obtaining at most five heads is
a.1/64
b.None of the above.
c.63/64
d.59/64
e.5/64

10.A basket contains five red balls, four white balls and three blue balls. Two balls are drawn, one after the other, with the first ball replaced before the second is drawn. Find the probability of drawing two white balls.
a.2/12=1/6
b.2/9
c.4/12=1/3
d.1/9
e.none of the above