Multiple choice question from Probability.

Choose the one alternative that best completes the statement or answer the question.
A student is studying mathematics and chemistry. The probability that he passes mathematics is 0.75, the probability that he fails chemistry is 0.2, and the probability that he passes mathematics but fails chemistry is 0.05.
1)The probability that he passes both courses is
a.0.
b.0.75.
c.0.60.
d.0.70.
e.none of the above

2)The probability that he either passes mathematics or fails chemistry is
a.0.15
b.0.90.
c.1.0.
d.0.95.
e.none of the above

3) If E and F are independent and Pr(E) = 0.3 and Pr(F) = 0.6, then
Pr (E υ F) is
a.0.18.
b.0.72.
c.0.90.
d.0
e. none of the above

4)Suppose that Pr (E) = 0.85, Pr (F) = 0.4, and Pr (E ∩ F) = 0.3. Then (F\E) =
a.3/10
b.3/4
c.6/17
d.6/11.
e.none of the above

5) Two cards are drawn (without replacement) from an ordinary deck of 52 cards. The probability that the second card is black if the first card is the ace of hearts is
a.2/51
b.26/51
c.1/104
d.1/2.
e.none of the above

The probability that person A will pass Finite Mathematics is 5/8 and the probability that person B will pass is 6/7.
Assume the events are independent.
6) In the situation above, the probability that neither will pass is
a.1.
b.3/56
c.29/56
d.53/56
e.None of the above

7) In the situation above, the probability that both will pass is
a.53/56
b.0.
c.15/28
d.30/54
e.none of the above

8) In the situation above, the probability that at least one will pass is
a.53/56
b.0.
c.13/28
d.30/56
e.none of the above

9)Based on the table above, the probability that a randomly-selected crime committed in a residential area is a murder is
a.10/17
b.1/5
c.4/35
d.34/175
e.none of the above

10)  Based on the table above, the probability that a randomly-selected crime was committed in a commercial area given that it was an assault is
a.1/3
b.1/7
c.2/15
d.2/5
e.none of the above

11)  Of the 1000 freshmen enrolled at a certain college, 100 have verbal SAT scores above 650. Thirty of these 100 students earned an A in freshman composition. The probability that a freshman has a verbal SAT score above 650 and earned an A in freshman composition is
a.1/10
b.3/100
c.13/100
d.Impossible to determine.
e.none of the above