Answer:
The statements that are true are (A), (D) and (G)
Explanation:
A. If A and B are mutually exclusive events, the probability for the event (A and B) is zero.
(A) is true, A and B can not happen together since they are mutually exclusive. P(A and B) is zero.
B. If an experiment has n possible outcomes, each outcome has probability 1n1n.
(B) is not true(probability of each outcome is 1/n)
C. In probability theory, an event is one possible outcome of an experiment.
(C) is not true( An event is not one possible outcome of an experiment)
D. The probability for an event may be zero.
(D) is true(If there is no chance for the event's occurrence)
E. If A and B are different events, the probability for the event (A and B) is zero.
(E) is not True(The probability A and B can be zero if only if A and B are mutually exclusive)
F. If an event has a probability of 50%, then, if the random experiment is carried out 100 times, it is unlikely, though not impossible, that the event will occur less than 10 times.
(F) is not true
G. If an event has a probability of 50%, then, if the random experiment is carried out 10 times, the event will occur exactly 5 times.
(G) is true(5/10 is 50%)
H. The probability for an event may be larger than 1.
(H) is not true(Maximum value for probability is 1, Certainty)
I. If event A has probability p1p1 and event B has probability p2p2, then the event (A or B) has probability p1+p2p1+p2.
(I) is not true
J. If a random experiment has n possible outcomes, then there are exactly 2n2n many events associated with the random experiment.
(J) is not true