1
GATE IN 2015
+2
-0.6
A coin is tossed thrice. Let $$X$$ be the event that head occurs in each of the first two tosses. Let $$Y$$ be the event that a tail occurs on the third toss. Let $$Z$$ be the event that two tails occur in three tosses. Based on the above information, which one of the following statements is TRUE?
A
$$X$$ and $$Y$$ are not independent
B
$$Y$$ and $$Z$$ are dependent
C
$$Y$$ and $$Z$$ are independent
D
$$X$$ and $$Z$$ are independent
2
GATE IN 2014
Numerical
+2
-0
Given that $$x$$ is a random variable in the range $$\left[ {0,\infty } \right]$$ with a probability density function $${{{e^{ - {x \over 2}}}} \over K},$$ the value of the constant $$K$$ is _______
3
GATE IN 2014
Numerical
+2
-0
The figure shown the schematic of a production process with machines $$A, B$$ and $$C.$$ An input job needs to be pre-processed either by $$A$$ or by $$B$$ before it is fed to $$C,$$ from which the final finished product comes out. The probabilities of failure of the machines are given as:
$${P_{\rm A}} = 0.15,\,\,{P_{\rm B}} = 0.05\,\,\& \,\,{P_C} = 0.1$$

Assuming independence of failures of the machines, the probability that a given job is successfully processed (up to the third decimal place) is _____.

4
GATE IN 2012
+2
-0.6
A fair coin is tossed till a head appears for the first time. The probability that the number of required tosses is odd, is
A
$$1/3$$
B
$$1/2$$
C
$$2/3$$
D
$$3/4$$
GATE IN Subjects
EXAM MAP
Medical
NEET