Discrete Mathematics
Q171.
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?Q172.
What is the probability that in a randomly chosen group of r people at least three people have the same birthday?Q173.
Aishwarya studies either computer science or mathematics everyday. If she studies computer science on a day, then the probability that the studies mathematics the next day is 0.6. If she studies mathematics on a day, then the probability that the studies computer science the next day is 0.4. Given that Aishwarya studies computer science on Monday, what is the probability that she studies computer science on Wednesday?Q174.
Consider a company that assembles computers. The probability of a faulty assembly of any computer is p. The company therefore subjects each computer to a testing process. This testing process gives the correct result for any computer with a probability of q. What is the probability of a computer being declared faulty?Q176.
A deck of 5 cards (each carrying a distinct number from 1 to 5) is shuffled thoroughly. Two cards are then removed one at a time from the deck. What is the probability that the two cards are selected with the number on the first card being one higher than the number on the second card?Q177.
Consider a finite sequence of random values X=[x_{1},x_{2},...,x_{n}]. Let \mu _{x} be the mean and \sigma _{x} be the standard deviation of X .Let another finite sequence Y of equal length be derived from this as y_{i}=a*x_{i}+b, where a and b are positive constants. Let Let \mu _{y} be the mean and \sigma _{y} be the standard deviation of this sequence. Which one of the following statements is INCORRECT?Q178.
The number of arrangements of six identical balls in three identical bins is ____.Q179.
Consider the sequence \langle x_n \rangle , \: n \geq 0 defined by the recurrence relation x_{n+1} = c . x^2_n -2, where c > 0. Suppose there exists a non-empty, open interval (a, b) such that for all x_0 satisfying a \lt x_0 \lt b, the sequence converges to a limit. The sequence converges to the value?Q180.
Consider the two statements. S1: There exist random variables X and Y such that \left(\mathbb E[(X-\mathbb E(X))(Y-\mathbb E(Y))]\right)^2 > \textsf{Var}[X]\textsf{Var}[Y] S2: For all random variables X and Y, \textsf{Cov}[X,Y]=\mathbb E \left[|X-\mathbb E[X]||Y-\mathbb E[Y]|\right ] Which one of the following choices is correct?