Test: Probability- 1 - Civil Engineering (CE) MCQ

# Test: Probability- 1 - Civil Engineering (CE) MCQ

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## 10 Questions MCQ Test Engineering Mathematics - Test: Probability- 1

Test: Probability- 1 for Civil Engineering (CE) 2024 is part of Engineering Mathematics preparation. The Test: Probability- 1 questions and answers have been prepared according to the Civil Engineering (CE) exam syllabus.The Test: Probability- 1 MCQs are made for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Probability- 1 below.
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Test: Probability- 1 - Question 1

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

Detailed Solution for Test: Probability- 1 - Question 1

Test: Probability- 1 - 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

Detailed Solution for Test: Probability- 1 - Question 2

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

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Test: Probability- 1 - Question 3

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

Detailed Solution for Test: Probability- 1 - Question 3

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

Test: Probability- 1 - Question 4

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

Detailed Solution for Test: Probability- 1 - Question 4

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

Test: Probability- 1 - 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

Detailed Solution for Test: Probability- 1 - Question 5

Constraints are

Test: Probability- 1 - 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

Detailed Solution for Test: Probability- 1 - Question 6

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.

Test: Probability- 1 - Question 7

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

What is P(A ∪ B)?

Detailed Solution for Test: Probability- 1 - Question 7

We know that:

Test: Probability- 1 - 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

Detailed Solution for Test: Probability- 1 - Question 8

Random variable assigns a real number to each possible outcome.

Let X be a discreet random variable,then

where V(x) is the variance of x,

Explanation:

• 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 called the variance of a random variable
• Variance measure how far a set of numbers is spread out
• A variance of zero(R=0) indicates that all the values are identical
• A variance of X = R =E[X2]- (E[X])This quantity is always non-negative as it is an expectation of a non-negative quantity
• A non-zero variance is always positive means R > 0

So, R ≥ 0 is the answer. Since variance is  and hence never negative,

Test: Probability- 1 - 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

Detailed Solution for Test: Probability- 1 - Question 9

The p.d.t of the random variable is

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

Test: Probability- 1 - Question 10

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

Detailed Solution for Test: Probability- 1 - Question 10

(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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## Engineering Mathematics

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