1
GATE EE 2010
+1
-0.3
A box contains $$4$$ white balls and $$3$$ red balls. In succession, two balls are randomly selected and removed from the box. Given that first removed ball is white, the probability that the $$2$$nd removed ball is red is
A
$$1/3$$
B
$$3/7$$
C
$$1/2$$
D
$$4/7$$
2
GATE EE 2009
+1
-0.3
Assume for simplicity that $$N$$ people, all born in April (a month of $$30$$ days) are collected in a room, consider the event of at least two people in the room being born on the same date of the month (even if in different years e.g. $$1980$$ and $$1985$$). What is the smallest $$N$$ so that the probability of this exceeds $$0.5$$ is ?
A
$$20$$
B
$$7$$
C
$$15$$
D
$$16$$
3
GATE EE 2008
+1
-0.3
$$X$$ is uniformly distributed random variable that take values between $$0$$ and $$1.$$ The value of $$E\left( {{X^3}} \right)$$ will be
A
$$0$$
B
$$1/8$$
C
$$1/4$$
D
$$1/2$$
4
GATE EE 2005
+1
-0.3
If $$P$$ and $$Q$$ are two random events, then which of the following is true?
A
Independence of $$P$$ and $$Q$$ implies that probability $$\,\,\left( {P \cap Q} \right) = 0\,\,$$
B
Probability $$\,\,\left( {P \cap Q} \right) \ge \,\,$$ probability $$(P)$$ $$+$$ probability $$(Q)$$
C
If $$P$$ and $$Q$$ are mutually exclusive then they must be independent
D
Probability $$\,\,\left( {P \cap Q} \right) \le \,\,$$ probability $$(P)$$
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