1
IIT-JEE 1996
MCQ (Single Correct Answer)
+2
-0.5
For the three events $$A, B,$$ and $$C,P$$ (exactly one of the events $$A$$ or $$B$$ occurs) $$=P$$ (exactly one of the two events $$B$$ or $$C$$ occurs)$$=P$$ (exactly one of the events $$C$$ or $$A$$ occurs)$$=p$$ and $$P$$ (all the three events occur simultaneously) $$= {p^2},$$ where $$0 < p < 1/2.$$ Then the probability of at least one of the three events $$A,B$$ and $$C$$ occurring is
A
$${{3p + 2{p^2}} \over 2}$$
B
$${{p + 3{p^2}} \over 4}$$
C
$${{p + 3{p^2}} \over 2}$$
D
$${{3p + 2{p^2}} \over 4}$$
2
IIT-JEE 1995 Screening
MCQ (Single Correct Answer)
+2
-0.5
The probability of India winning a test match against West Indies is $$1/2$$. Assuming independence from match to match the probability that in a $$5$$ match series India's second win occurs at third test is
A
$$1/8$$
B
$$1/4$$
C
$$1/2$$
D
$$2/3$$
3
IIT-JEE 1995 Screening
MCQ (Single Correct Answer)
+2
-0.5
Three of six vertices of a regular hexagon are chosen at random. The probability that the triangle with three vertices is equilateral, equals
A
$$1/2$$
B
$$1/5$$
C
$$1/10$$
D
$$1/20$$
4
IIT-JEE 1994
MCQ (Single Correct Answer)
+2
-0.5
Let $$A, B, C$$ be three mutually independent events. Consider the two statements $${S_1}$$ and $${S_2}$$
$${S_1}\,:\,A$$ and $$B \cup C$$ are independent
$${S_2}\,:\,A$$ and $$B \cap C$$ are independent
Then,
A
Both $${S_1}$$ and $${S_2}$$ are true
B
Only $${S_1}$$ is true
C
Only $${S_2}$$ is true
D
Neither $${S_1}$$ nor $${S_2}$$ is true
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