Discrete Mathematics
Q141.
Let G be a simple connected planar graph with 13 vertices and 19 edges. Then, the number of faces in the planar embedding of the graph is:Q142.
A class of 30 students occupy a classroom containing 5 rows of seats, with 8 seats in each row. If the students seat themselves at random, the probability that sixth seat in the fifth row will be empty is:Q144.
Let G be a simple undirected planar graph on 10 vertices with 15 edges. If G is a connected graph, then the number of bounded faces in any embedding of G on the plane is equal toQ145.
Two people, P and Q, decide to independently roll two identical dice, each with 6 faces, numbered 1 to 6. The person with the lower number wins. In case of a tie, they roll the dice repeatedly until there is no tie. Define a trial as a throw of the dice by P and Q. Assume that all 6 numbers on each dice are equi-probable and that all trials are independent. The probability (rounded to 3 decimal places) that one of them wins on the third trial isQ146.
Suppose X_{i} for i =1,2,3 are independent and identically distributed random variables whose probability mass functions are Pr[X_{i}=0]=Pr[X_{i}=1]=1/2 for i=1,2,3. Define another random variable Y=X_{1}X_{2}\oplus X_{3}, \; where \; \oplus denotes XOR. Then Pr[Y=0|X_{3}=0]=_______________.Q147.
Let A and B be any two arbitrary events, then, which one of the following is TRUE?Q148.
Each of the nine words in the sentence "The quick brown fox jumps over the lazy og" is written on a separate piece of paper. These nine pieces of paper are kept in a box. One of the pieces is drawn at random from the box. The expected length of the word drawn is _____________. (The answer should be rounded to one decimal place)Q149.
A probability density function on the interval [a,1] is given by 1/x^{2} and outside this interval the value of the function is zero.The value of a is __________.