Discrete Mathematics


Q161.

Let P(E) denote the probability of the occurrence of event E. If P(A)= 0.5 and P(B)=1 then the values of P(A|B) and P(B|A) respectively are
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Q162.

Suppose p is the number of cars per minute passing through a certain road junction between 5 PM and 6 PM, and p has a Poisson distribution with mean 3. What is the probability of observing fewer than 3 cars during any given minute in this interval?
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Q163.

Suppose a fair 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 total of values that turn up is at least 6?
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Q164.

Consider a random variable X that 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
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Q165.

Let f(x) be the continuous probability density function of a random variable x, the probability that a \lt x \leq b, is :
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Q166.

If the difference between the expectation of the square of random variable (E[X^{2}]) and the square of the expectation of the random variable (E[X^{2}]) is denoted by R then
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Q167.

An unbalanced dice (with 6 faces, numbered from 1 to 6) is thrown. The probability that the face value is odd is 90% of the probability that the face value is even. The probability of getting any even numbered face is the same. If the probability that the face is even given that it is greater than 3 is 0.75, which one of the following options is closest to the probability that the face value exceeds 3?
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Q168.

If the pdf of a Poisson distribution is given by f(x) = \frac{e^{-2} 2^x}{x!}then its mean is
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Q169.

Three coins are tossed simultaneously. The probability that they will fall two heads and one tail is
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Q170.

A sample space has two events A and B such that probabilities P(A\cap B) = \dfrac{1}{2}, P(A') = \dfrac{1}{3}, P(B') =\dfrac{1}{3}. What is P(A\cup B) ?
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