GATE Questions & Answers of Probability and Statistics Electronics and Communication Engg

Three fair cubical dice are thrown simultaneously. The probably that all three dice have the same number of dots on the faces showing us is (up to third decimal place) ____________.

The second moment of a Poisson-distributed random variable is 2. The mean of the random variable is _______ 

Two random variables X and Y are distributed according to

fX,Yx,y=x+y,   0x1, 0y10,         otherwise

The probability PX+Y1 is ________

The probability of getting a “head” in a single toss of a biased coin is 0.3. The coin is tossed  repeatedly till a “head” is obtained. If the tosses are independent, then the probability of getting “head” for the first time in the fifth toss is __________

Suppose $ A $ and $ B $ are two independent events with probabilities $ P(A)\neq0 $ and $ P(B)\neq0 $. Let A and B be their complements Which of the following statement is FALSE?

In a housing society, half of the families have a single child per family, while the remaining half have two children per family. The probability that a child picked at random, has a sibling is _____

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

A fair coin is tossed repeatedly till both head and tail appear at least once. The average number of tosses required is ______

Parcels from sender S to receiver R pass sequentially through two post-offices. Each post-office has a probability 15 of losing an incoming parcel, independently of all other parcels. Given that a parcel is lost, the probability that it was lost by the second post-office is_________.

A fair coin is tossed till a head appears for the first time. The probability that the number of required tosses is odd, is

A fair coin is tossed 10 times. What is the probability that ONLY the first two tosses will yield heads?

An examination consists of two papers, Paper 1 and Paper 2. The probability of failing in Paper 1 is 0.3 and that in Paper 2 is 0.2. Given that a student has failed in Paper 2, the probability of failing in Paper 1 is 0.6. The probability of a student failing in both the papers is