1
IIT-JEE 1994
+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
2
IIT-JEE 1993
+1
-0.25
An unbiased die with faces marked $$1,2,3,4,5$$ and $$6$$ is rolled four times. Out of four face values obtained, the probability that the minimum face value is not less than $$2$$ and the maximum face value is not greater than $$5,$$ is then:
A
$$16/81$$
B
$$1/81$$
C
$$80/81$$
D
$$65/81$$
3
IIT-JEE 1992
+2
-0.5
India plays two matches each with West Indies and Australia. In any match the probabilities of India getting, points $$0,$$ $$1$$ and $$2$$ are $$0.45, 0.05$$ and $$0.50$$ respectively. Assuming that the outcomes are independent, the probability of India getting at least $$7$$ points is
A
$$0.8750$$
B
$$0.0875$$
C
$$0.0625$$
D
$$0.0250$$
4
IIT-JEE 1988
+2
-0.5
One hundred identical coins, each with probability, $$p,$$ of showing up heads are tossed once. If $$0 < p < 1$$ and the probability of heads showing on $$50$$ coins is equal to that of heads showing on $$51$$ coins, then the value of $$p$$ is
A
$$1/2$$
B
$$49/101$$
C
$$50/101$$
D
$$51/101.$$
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