1
GATE PI 2015
MCQ (Single Correct Answer)
+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 PI 2014
Numerical
+2
-0
A simple random sample of $$100$$ observations was taken form a large population. The sample mean and the standard deviation were determined to be $$80$$ and $$12,$$ respectively. The standard error of mean is ______.
Your input ____
3
GATE PI 2014
MCQ (Single Correct Answer)
+2
-0.6
Marks obtained by $$100$$ students in an examination are given in the table GATE PI 2014 Engineering Mathematics - Probability and Statistics Question 5 English

What would be the mean, median, and mode of the marks obtained by the students?

A
Mean $$33;$$ Median $$35;$$ Mode $$40$$
B
Mean $$35;$$ Median $$32.5;$$ Mode $$40$$
C
Mean $$33;$$ Median $$35;$$ Mode $$35$$
D
Mean $$35;$$ Median $$32.5;$$ Mode $$35$$
4
GATE PI 2012
MCQ (Single Correct Answer)
+2
-0.6
A box contains $$4$$ red balls and $$6$$ black balls. Three balls are selected randomly from the box one after another, without replacement. The probability that the selected set contains one red ball and two black balls is
A
$$1/20$$
B
$$1/12$$
C
$$3/10$$
D
$${\raise0.5ex\hbox{$\scriptstyle 1$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle 2$}}$$
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