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q1)
Suppose that 10,000 tickets are sold in one lottery and 5000 tickets are sold in another lottery. If a person owns 100 tickets in each lottery, what is the probability that she will win at least one first prize?
a) .02
b) .03
c) .01
d) .0002
q2)
Bus tickets in a certain city contain four numbers, U, V , W, and X. Each of these numbers is equally likely to be any of the 10 digits 0, 1, . . . , 9, and the four numbers are chosen independently. A bus rider is said to be lucky if U + V =W + X. What proportion of the riders are lucky?
a) 6.7%
b) 2.85%
c) 94.3%
d) 97.15%
q3)
Suppose thatA, B, andD are any three events such that Pr(A|D) ≥ Pr(B|D) and Pr(A|Dc) ≥ Pr(B|Dc). Then
a) Pr(A) > Pr(B).
b) Pr(A) ≥ Pr(B).
c) Pr(A) = Pr(B).
d) Cannot be determined
q4)
Picture there being 3 light bulbs and 4 doors, 2 doors lead to the light bulb on the left, and the other 2 doors lead to 1 of the light bulbs each. If the bulbs light up randomly, what’s the probability of walking through a door into a lit up room?
a) ½
b) ¼
c) 1/3
d) None of these
. q5)
I have two children, one of whom is a son born on a Tuesday. What is the probability that I have two boys?
a) ½
b) 1/3
c) ¼
d) None of the above
q6)
Three prisoners A, B, and C on death row know that exactly two of them are going to be executed, but they do not know which two. Prisoner A knows that the jailer will not tell him whether or not he is going to be executed. He therefore asks the jailer to tell him the name of one prisoner other than A himself who will be executed. The jailer responds that B will be executed. Upon receiving this response, Prisoner A reasons as follows: Before he spoke to the jailer, the probability was 2/3 that he would be one of the two prisoners executed. After speaking to the jailer, he knows that either he or prisoner C will be the other one to be executed. Hence, the probability that he will be executed is now only 1/2. Thus, merely by asking the jailer his question, the prisoner reduced the probability that he would be executed from 2/3 to 1/2, because he could go through exactly this same reasoning regardless of which answer the jailer gave.
a) prisoner A’s reasoning is correct.
b) prisoner A’s reasoning is incorrect.
c) prisoner A’s probability of getting executed is 1/3 instead
d) prisoner A’s probability of getting executed cannot be calculated.
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Locked
