1
IIT-JEE 1998
+2
-0.5
Seven white balls and three black balls are randomly placed in a row. The probability that no two black balls are placed adjacently equals
A
$$1/2$$
B
$$7/15$$
C
$$2/15$$
D
$$1/3$$
2
IIT-JEE 1998
+2
-0.5
A fair coin is tossed repeatedly. If the tail appears on first four tosses, then the probability of the head appearing on the fifth toss equals
A
$$1/2$$
B
$$1/32$$
C
$$31/32$$
D
$$1/5$$
3
IIT-JEE 1996
+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
$${{3p + 2{p^2}} \over 4}$$
4
IIT-JEE 1995 Screening
+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
$$2/3$$
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