Probability Theory
Q31.
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?Q32.
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 areQ33.
Let f(x) be the continuous probability density function of a random variable x, the probability that a \lt x \leq b, is :Q34.
If the pdf of a Poisson distribution is given by f(x) = \frac{e^{-2} 2^x}{x!}then its mean isQ35.
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 thenQ36.
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?Q37.
Three coins are tossed simultaneously. The probability that they will fall two heads and one tail isQ38.
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) ?Q39.
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?Q40.
What is the probability that in a randomly chosen group of r people at least three people have the same birthday?