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27 Sep 2010, 08:48
Kudos
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
73% (01:18) correct
27%
(01:25)
wrong
based on 132
sessions
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Not Attempted Yet
S = {1, 2, 3}
T = {4, 5, 6, 7}
What is the probability that x chosen from S and y chosen from T will result x*y = even
A. 1/3
B. 2/3
C. 1/2
D. 5/6
E. 1/6
T = {4, 5, 6, 7}
What is the probability that x chosen from S and y chosen from T will result x*y = even
A. 1/3
B. 2/3
C. 1/2
D. 5/6
E. 1/6
27 Sep 2010, 08:59
Kudos
Bookmarks
rxs0005
The product of two integers to be even either one (or both) must be even.
So we need probability of choosing even from S OR even from T.
NOTE: Probability of A OR B.
If Events A and B are independent, the probability that either Event A or Event B occurs is:
P(A or B) = P(A) + P(B) - P(A and B) = P(A) + P(B) - P(A)*P(B)
When we say "A or B occurs" we include three possibilities:
A occurs and B does not occur;
B occurs and A does not occur;
Both A and B occur.
So as \(P(S_{even})=\frac{1}{3}\) and \(P(T_{even})=\frac{2}{4}=\frac{1}{2}\) then \(P(S_{even} \ or \ T_{even})=\frac{1}{3}+\frac{1}{2}-\frac{1}{3}*\frac{1}{2}=\frac{2}{3}\).
OR there are 12 pairs possible and out them 8 have either one or both numbers even, so \(P=\frac{8}{12}=\frac{2}{3}\).
Answer: B.
