Engineering Maths · all questions

Probability and Statistics
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Q41

A fair dice is rolled twice. The probability that an odd number will follow an even number is

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Q42

Two bags A and B have equal number of bails. Bag A has 20% red balls and 80% green bails. Bag B has 30% red bails. 60% green balls and 10% yellow balls. Contents of Bags A and B are mixed thoroughly and a ball is randomly picked from the mixture. What is the chance that the ball picked is red?

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Q43

If two fair coins are flipped and at least one of the outcomes is known to be a head, what is the probability that both outcomes are heads?

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Q44

If the standard deviation of the spot speed of vehicles in a highway is 8.8 kmph and the mean speed of the vehicles is 33 kmph, the coefficient of variation in speed is

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Q45

Which one of the following statements is NOT true?

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Q46

The probability that a thermistor randomly picked up from a production unit is defective is 0.1. The probability that out of 10 thermistors randomly picked up, 3 are defective is

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Q47

In a game, two players X and Y are tossing a coin alternately. Whoever gets a 'head' first, wins the game and the game is terminated. Find the chance that player X will win the game if he starts?

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Q48

A loaded dice has following probability distribution of occurrences

Dice Value	1	2	3	4	5	6
Probability	$\frac{1}{4}$	$\frac{1}{8}$	$\frac{1}{8}$	$\frac{1}{8}$	$\frac{1}{8}$	$\frac{1}{4}$

If three identical dice as the above are thrown, the probability of occurrence of values 1, 5 and 6 on the three dice is

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Q49

Consider a Gaussian distributed random variable with zero mean and standard deviation σ. The value of its cumulative distribution function at the origin will be

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Q50

Two independent random variables X and Y are uniformly distributed in the interval [-1, 1]. The probability that max [X, Y] is less than

\frac{1}{2}

is

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Q51

An unbiased coin is tossed an infinite number of times. The probability that the fourth head appears at the tenth toss is

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Q52

The standard deviation of a uniformly distributed random variable between 0 and 1 is

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Q53

X and Y are two random independent events. It is known that P(X) = 0.40 and

P (X \cup Y^{C}) = 0.7.

Which one of the following is the value of

P (X \cup Y) ?

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Q54

A screening test is carried out to detect a certain disease. It is found that 12% of the positive reports and 15% of the negative reports are incorrect. Assuming that the probability of a person getting a positive report is 0.01, the probability that a person tested gets in incorrect report is

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Q55

Suppose afair six-sided die is rolled once. If the value on the die is 1, 2 or 3 the die is rolled a second time. What is the probability that the sum of total values that turn up is at least 6?

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Q56

If X is a discrete random variable that follows Binomial distribution, then which one of the following response relations is correct?

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Q57

The number of parameters in the univariate exponential and Gaussian distributions, respectively, are

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Q58

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

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Q59

The probability density function of a continuous random variable distributed uniformly between x and y (for y > x) is

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Q60

If P(x) =

\frac{1}{4}

, P(Y) =

\frac{1}{3}

and

P (X \cap Y) = \frac{1}{12},

the value of

P (\frac{Y}{X})

is

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