Theoretical Probability

A ball is drawn randomly from a jar containing 6 red marbles, 2 white marbles, and 5 yellow marbles. Find the probability of:

1. Drawing a white marble.

2. Drawing a red marble.

3. Drawing a green marble.

4. Drawing two yellow marbles if you draw with replacement.

5. Drawing first a red marble then a white marble if marbles are drawn without replacement.

Compute the probability of tossing a fair six-sided die and getting:

1. an even number.

2. a number less than 3.

Compute the probability of rolling a fair 12-sided die and getting:

1. a number other than 8.

2. a 2 or 7.

A fair six-sided die is rolled twice. What is the probability of getting:

1. a 6 on both rolls?

2. a 5 on the first roll and an even number on the second roll?

Suppose that 21% of people own dogs. If you pick two people at random, what is the probability that neither own a dog?

At some random moment, you look at your digital clock and note the minutes reading.

1. What is probability the minutes reading is 15?

2. What is the probability the minutes reading is 15 or less?

What is the probability of flipping a fair coin three times

1. and getting a head each time?

2. not getting a head at all?

What is the probability of rolling two fair six-sided dice

1. and getting a sum greater than or equal to 7?

2. getting an even sum or a sum greater than 7?

A box contains four black pieces of cloth, two striped pieces, and six dotted pieces. A piece is selected randomly and then placed back in the box. A second piece is selected randomly. What is the probability that:

1. both pieces are dotted?

2. the first piece is black, and the second piece is dotted?

3. one piece is black, and one piece is striped?

Compute the probability of rolling five fair six-sided dice (each side has equal probability of landing face up on each roll) and getting:

1. a 3 on all five dice.

2. at least one of the die shows a 3.

If you pick a card from a standard deck of 52 cards, what is the probability of getting

1. a 7?

2. a club?

3. a spade or a club?

4. a diamond or a 5?

A box of chocolates contains 7 dark chocolate pieces and 3 milk chocolate pieces (and no others). If you randomly pick 2 pieces and eat each chocolate after choosing it, what is the probability of choosing at least one dark chocolate? Write the probability in all three forms.

A bag contains 3 green marbles, 4 red marbles, and 5 blue marbles (and no others). If you randomly pull out three marbles all at once, what is the probability that you choose 3 blue marbles? Write the probability in all three forms.

A bag contains 3 green marbles, 4 red marbles, and 5 blue marbles (and no others). If you randomly pull out a marble and put the marble back 3 times, what is the probability that you pull out a blue marble all 3 times? Write the probability in all three forms.

A bag contains 3 green marbles, 4 red marbles, and 5 blue marbles (and no others). If you randomly pull out three marbles all at once, what is the probability that you choose at least 1 blue marble? Write the probability in all three forms.