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Test: Probability- 1


10 Questions MCQ Test GATE Electrical Engineering (EE) 2023 Mock Test Series | Test: Probability- 1


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Attempt Test: Probability- 1 | 10 questions in 30 minutes | Mock test for GATE preparation | Free important questions MCQ to study GATE Electrical Engineering (EE) 2023 Mock Test Series for GATE Exam | Download free PDF with solutions
QUESTION: 1

Let A and B be any two arbitrary events, then, which one of the following is true?

Solution:

QUESTION: 2

A bag contains 10 white balls and 15 black balls. Two balls are drawn in succession. The probability that one of them is black and the other is white is

Solution:


Bag contains 10 white balls and 15 black balls. Required probability

QUESTION: 3

Two dice are thrown simultaneously. The probability that at least one of them will have 6 facing up is 

Solution:

P(atleast one of dice will have 6 facing 
= 1 - P(none of dice have 6 facing up)

QUESTION: 4

The probability that top and bottom cards of a randomly shuffled deck are both aces is-
Solution:

The probability that the bottom card of a randomly shuffled deck is ace = 4/52 because there are 4 aces out of total 52 cards.
From the remaining 3 aces out of SVcards the probability that the top card is also an ace = 3/51.
So required probability 

QUESTION: 5

E1 and E2 are events in a probability space satisfying the following constraints:

The value of Pr(E1), the probability of the event E1, is
Solution:

Constraints are

QUESTION: 6

A program consists of two modules executed sequentially. Let f1(t) and f2(t) respectively denote the probability density functions of time taken to execute the two modules. The probability density function of the overall time taken to execute the program is given by
Solution:

Let the time taken for first and second modules be represented by x and y and total time = t.
∴ t = x + y is a random variable.
Now the joint density function

which is also called as convolution of f1 and f2, abbreviated as f1 * f2.

QUESTION: 7

 A sample space has two events A and B such that probabilities

What is P(A ∪ B)?
Solution:

We know that:

QUESTION: 8

If the difference between the expectation of the square of a random variable (E[x2] and the square of the expectation of the random variable (E[x])2 is denoted by R, then
Solution:


where V(x) is the variance of x,
Since variance is  and hence never negative, 

QUESTION: 9

Consider a random variable Xthat takes values +1 and -1 with probability 0.5 each. The values of the cumulative distribution function F(x) at x = -1 and +1 are
Solution:

The p.d.t of the random variable is

The cumulative distribution function F(x) is the probability uptox as given below:

QUESTION: 10

If P and Q are two random events, then the following is TRUE
Solution:

(a) is false since of Pand Q are independent

which need not be zero.
(b) is false since

(c) is false since independence and mutually exclusion are unrelated properties.
(d) is true

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