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) ____________.
Two random variables X and Y are distributed according to
${f}_{X,Y}\left(x,y\right)=\left\{\begin{array}{l}\left(x+y\right),0\le x\le 1,0\le y\le 1\\ 0,otherwise\end{array}\right.$
The probability $P\left(X+Y\le 1\right)$ is ________
Suppose $ A $ and $ B $ are two independent events with probabilities $ P(A)\neq0 $ and $ P(B)\neq0 $. Let $\overline{)A}$ and $\overline{)B}$ 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 $\frac{1}{5}$ 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