Probability: Sample Space of Rolling Two Dice

Play an AI-generated podcast conversation about this lesson

What is the sample space of rolling two dice?

36 points (correct)

6 points

24 points

12 points

What is the event E = {H} in a coin flip?

The event that a tail appears

The event that a head appears (correct)

The event that the coin is lost

The event that the coin lands on its edge

What is the event E = {2, 4, 6} in a die roll?

The event that a prime number appears

The event that an odd number appears

The event that an even number appears (correct)

The event that the die lands on its edge

What is the sample space of measuring the lifetime of a car?

All nonnegative real numbers Signup and view all the answers

What does the notation [a, b] represent?

The set of all points x such that a ≤ x ≤ b Signup and view all the answers

What is an event in a probability experiment?

A subset of the sample space Signup and view all the answers

What is the probability that each typist is chosen to do the work?

1/3 Signup and view all the answers

What is the expression for E[A] in terms of E[Tx] and probabilities?

E[A] = 1 - p1 - px / (1 + E[Tx])(1 - p1) Signup and view all the answers

In a multinomial trial, what is the sum of the probabilities of each outcome?

1 Signup and view all the answers

What is the condition for obtaining E[T(i1,..., ir)] in the nonoverlapping case?

If (i1,..., ir) is nonoverlapping Signup and view all the answers

What is the variance of a Poisson random variable with mean 3?

3 Signup and view all the answers

What is the purpose of introducing x in the pattern Px = (i1,..., in, x)?

To obtain the mean occurrence time of the pattern P Signup and view all the answers

What is the conditional probability of Xi given that X2 > 0?

pi/(1 - p0) Signup and view all the answers

What is the relationship between E[Tx] and E[T]?

E[Tx] = E[T] + E[A] Signup and view all the answers

What is the expected value of the number of successes in n trials, given that the success probability is u?

nu Signup and view all the answers

What is the expression for E[T] in terms of px and p1?

E[T] = (1/p1)n - 1 / (1 - p1) Signup and view all the answers

What happens when the pattern i1,..., in includes all distinct data values?

We let x be a data value that is not in the pattern Signup and view all the answers

What is the basis for determining the lowest numbered card that has not yet appeared?

The upturned cards Signup and view all the answers

What is the purpose of turning the cards face up until the lowest numbered card appears?

To represent the first cycle Signup and view all the answers

What is the variable Xi in part (e) of the exercise equal to?

1 if one of the cycles ends with card i, and 0 otherwise Signup and view all the answers

What is the result of taking the first door in the prisoner's cell?

Return to the cell after two days Signup and view all the answers

What is the purpose of finding the variance of the number of cycles?

To understand the distribution of the number of cycles Signup and view all the answers

What is the third door in the prisoner's cell?

A path to freedom Signup and view all the answers

What is the probability of the ith person chosen being in favor?

Np/N Signup and view all the answers

What is Var n Xi?

n * Var(Xi) + 2 * Cov(Xi, Xj) Signup and view all the answers

What is E(N) equal to?

∞ Signup and view all the answers

What is P{N i} equal to?

(n - i + 1) / n Signup and view all the answers

What is the probability that the graph is connected?

(n - 1)!n / n! Signup and view all the answers

What is the approximate probability that a Poisson random variable with mean n is less than its mean?

1/2 Signup and view all the answers