Official PYQ · 2021Set 1 · Q27Probability and StatisticsMCQ2 marks

GATE EC 2021 Set 1 Q27 — Probability and Statistics

A box contains the following three coins.

A fair coin with head on one face and tail on the other face.
A coin with heads on both the faces.
A coin with tails on both the faces.

A coin is picked randomly from the box and tossed. Out of the two remaining coins in the box, one coin is then picked randomly and tossed. If the first toss results in a head, the probability of getting a head in the second toss is

View answer

Answer: B

Worked explanation not available yet.

Free practice · Your answers on this page are not saved.

Published 10 Oct 2026

Report a correction

GATE EC · 2026Probability and Statistics
Let $X, N, Y$ and $Z$ be random variables. The variables $X$ and $N$ are independent of each other. $X$ is uniformly distributed between $-1$ and $1 ; N$ follows Normal distribution with zero mean and unity variance. $Y$ and $Z$ are defined as, $Y=X+N$ and $Z=X^{2}+N$ . Which of the following pairs represents the values of correlation …
MCQ · 2 marks
GATE EC · 2025Probability and Statistics
A pot contains two red balls and two blue balls. Two balls are drawn from this pot randomly without replacement. What is the probability that the two balls drawn have different colours?
MCQ · 1 mark
GATE EC · 2025Probability and Statistics
A source transmits symbol $S$ that takes values uniformly at random from the set $\{-2,0,2\}$ . The receiver obtains $Y=S+N$ , where $N$ is a zero-mean Gaussian random variable independent of $S$ . The receiver uses the maximum likelihood decoder to estimate the transmitted symbol $S$ . Suppose the probability of symbol estimation error $P_{e}$ is …
MCQ · 2 marks
GATE EC · 2025Probability and Statistics
The random variable $X$ takes values in $\{-1,0,1\}$ with probabilities $P(X=-1)=P(X=1)=\alpha$ and $P(X=0)=1-2 \alpha$ , where $0<\alpha<1 / 2$ . Let $g(\alpha)$ denote the entropy of $X$ (in bits), parameterized by $\alpha$ . Which of the following statements is/are TRUE?
MSQ · 2 marks
GATE EC · 2025Probability and Statistics
Two fair dice (with faces labeled $1,2,3,4,5$ , and $6$ ) are rolled. Let the random variable $X$ denote the sum of the outcomes obtained. The expectation of $X$ is __________ (rounded off to two decimal places).
NAT · 2 marks
GATE EC · 2024Probability and Statistics
Suppose $\text{X}$ and $\text{Y}$ are independent and identically distributed random variables that are distributed uniformly in the interval $[0,1]$ . The probability that $\text{X} \geq \text{Y}$ is $\_\_\_\_\_\_$ .
NAT · 1 mark

Browse this topic

More Probability and Statistics questions

GATE EC 2021 Set 1 Q27 — Probability and Statistics

Related questions