1
IIT-JEE 1998
MCQ (Single Correct Answer)
+2
-0.5
If $$E$$ and $$F$$ are events with $$P\left( E \right) \le P\left( F \right)$$ and $$P\left( {E \cap F} \right) > 0,$$ then
A
occurrence of $$E$$ $$ \Rightarrow $$ occurrence of $$F$$
B
occurrence of $$F$$ $$ \Rightarrow $$ occurrence of $$E$$
C
non-occurrence of $$E$$ $$ \Rightarrow $$ non-occurrence of $$F$$
D
none of the above implications holds
2
IIT-JEE 1998
MCQ (Single Correct Answer)
+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
$$1/3$$
3
IIT-JEE 1998
MCQ (Single Correct Answer)
+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
$$1/5$$
4
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
$${{3p + 2{p^2}} \over 4}$$
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