Question 1

You ﬂip a coin. If it lands heads, you lose 1 point. If it lands tails, you ﬂip the coin again, and lose 1 point

Accepted Answer

The answer of You ﬂip a coin. If it lands...

Question 2

a bowl has eight ping pong balls numbered 1, 2, 2, 3, 4, 5, 5, 5. You pick a ball at random.
-Find p(the number on the ball drawn is $\geq 3$ ).

Accepted Answer

The answer of a bowl has eight ping pong balls...

Question 3

a bowl has eight ping pong balls numbered 1, 2, 2, 3, 4, 5, 5, 5. You pick a ball at random.
-Find E(X), where X = the number on the ball you draw.

Accepted Answer

The answer of a bowl has eight ping pong balls...

Question 4

A pair of dice, each with the numbers 1, 2, 2, 3, 3, 3 on its six sides are rolled. (a) What is the expected value of the sum of the numbers showing? (b) What is the expected value of the product of the numbers showing in part (a)?

Accepted Answer

The answer of A pair of dice, each with the...

Question 5

A die has the numbers 1, 2, 2, 3, 3, 3 on its six sides. If the die is rolled, what is the expected value and variance of the number showing?

Accepted Answer

The answer of A die has the numbers 1, 2,...

Question 6

You have seven cards, numbered 3 through 9, and you pick one at random. If you pick a card with a prime number, you get 1 point; if you pick a card with a composite number, you lose 1 point. Find the expected value of the number of points you get.

Accepted Answer

The answer of You have seven cards, numbered 3 through...

Question 7

Each of 26 cards has a diﬀerent letter of the alphabet on it. You pick one card at random. A vowel is worth 3 points and a consonant is worth 0 points. Let X = the value of the card picked. Find E(X), V (X), and the standard deviation of X .

Accepted Answer

The answer of Each of 26 cards has a diﬀerent...

Question 8

a bowl has eight ping pong balls numbered 1, 2, 2, 3, 4, 5, 5, 5. You pick a ball at random.
-Find p(the number on the ball drawn is even).

Accepted Answer

The answer of a bowl has eight ping pong balls...

Question 9

You have two decks of 26 cards. Each card in each of the two decks has a diﬀerent letter of the alphabet on it. You pick at random one card from each of the two decks. A vowel is worth 3 points and a consonant is worth 0 points. Let X = the sum of the values of the two cards picked. Find E(X), V (X), and the standard deviation of X .

Accepted Answer

The answer of You have two decks of 26 cards....

Question 10

Urn 1 contains 2 blue tokens and 8 red tokens; urn 2 contains 12 blue tokens and 3 red tokens. You roll a die to determine which urn to choose: if you roll a 1 or 2 you choose urn 1; if you roll a 3, 4, 5, or 6 you choose urn 2. Once the urn is chosen, you draw out a token at random from that urn. Given that the token is blue, what is the probability that the token came from urn 1?

Accepted Answer

The answer of Urn 1 contains 2 blue tokens and...

Quiz 7: A: Discrete Probability

You ﬂip a coin. If it lands heads, you lose 1 point. If it lands tails, you ﬂip the coin again, and lose 1 point

a bowl has eight ping pong balls numbered 1, 2, 2, 3, 4, 5, 5, 5. You pick a ball at random. -Find p(the number on the ball drawn is ≥3\geq 3≥3 ).

a bowl has eight ping pong balls numbered 1, 2, 2, 3, 4, 5, 5, 5. You pick a ball at random. -Find E(X), where X = the number on the ball you draw.

A pair of dice, each with the numbers 1, 2, 2, 3, 3, 3 on its six sides are rolled. (a) What is the expected value of the sum of the numbers showing? (b) What is the expected value of the product of the numbers showing in part (a)?

A die has the numbers 1, 2, 2, 3, 3, 3 on its six sides. If the die is rolled, what is the expected value and variance of the number showing?

You have seven cards, numbered 3 through 9, and you pick one at random. If you pick a card with a prime number, you get 1 point; if you pick a card with a composite number, you lose 1 point. Find the expected value of the number of points you get.

Each of 26 cards has a diﬀerent letter of the alphabet on it. You pick one card at random. A vowel is worth 3 points and a consonant is worth 0 points. Let X = the value of the card picked. Find E(X), V (X), and the standard deviation of X .

a bowl has eight ping pong balls numbered 1, 2, 2, 3, 4, 5, 5, 5. You pick a ball at random. -Find p(the number on the ball drawn is even).

a bowl has eight ping pong balls numbered 1, 2, 2, 3, 4, 5, 5, 5. You pick a ball at random. -Find p(the number on the ball drawn is $\geq 3$ ).