1
GATE CSE 2005
MCQ (Single Correct Answer)
+1
-0.3
Let $$f(x)$$ be the continuous probability density function of a random variable X. The probability that $$a\, < \,X\, \le \,b$$, is:
A
$$f\,(b - a)$$
B
$$f(b)\, - \,f(a)$$
C
$$\int\limits_a^b f (x)\,dx$$
D
$$\int\limits_a^b {xf} (x)\,dx$$
2
GATE CSE 2004
MCQ (Single Correct Answer)
+1
-0.3
In a population of N families, 50% of the families have three children, 30% of the families have two children and the remaining families have one child. What is the probability that a randomly picked child belongs to a family with two children ?
A
$$\,{3 \over {23}}$$
B
$$\,{6 \over {23}}$$
C
$$\,{3 \over {10}}$$
D
$$\,{3 \over {5}}$$
3
GATE CSE 2004
MCQ (Single Correct Answer)
+1
-0.3
If a fair coin is tossed four times, what is the probability that two heads and two tails will result?
A
3/8
B
$${\raise0.5ex\hbox{$\scriptstyle 1$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle 2$}}$$
C
5/8
D
3/4
4
GATE CSE 2003
MCQ (Single Correct Answer)
+1
-0.3
Let P(E) denote the probability of the event E. Given P(A) = 1, P(B) = $${\raise0.5ex\hbox{$\scriptstyle 1$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle 2$}}$$, the values of $$P\,(A\,\left| {B) \,} \right.$$ and $$P\,(B\,\left| {A) \,} \right.$$ respectively are
A
$${\raise0.5ex\hbox{$\scriptstyle 1$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle 4$}},\,{\raise0.5ex\hbox{$\scriptstyle 1$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle 2$}}$$
B
$${\raise0.5ex\hbox{$\scriptstyle 1$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle 2$}},\,{\raise0.5ex\hbox{$\scriptstyle 1$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle 4$}}$$
C
$${\raise0.5ex\hbox{$\scriptstyle 1$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle 2$}},\,1$$
D
$$1,\,\,{\raise0.5ex\hbox{$\scriptstyle 1$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle 2$}}$$
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