1) Write out the sample space for rolling a single standard die.

2) Find the following probabilities when rolling a single standard die (write your answers in both fraction AND percentage form for credit):

a) The probability of rolling a 3?
b) The probability of rolling an even number?
c) The probability of rolling at least a 3?
d) The probability of rolling a number less than 3?
e) The probability of rolling an 8?
f) The probability of rolling an a number less than 10?
g) The probability of not rolling a 6?

3) Write out the sample space for flipping a standard coin twice?

4) Find the following probabilities when flipping a standard coin twice? (write your answers in both fraction AND percentage form for credit):

a) The probability of getting both heads?
b) The probability of getting heads followed by tails?
c) The probability of getting heads on the first flip?
d) The probability of getting 1 heads and 1 tails?
e) The probability of getting at least one tails?
f) The probability of not getting any heads?

5) Write out the sample space for flipping a standard coin three times?

6) Find the following probabilities when flipping a standard coin three times (write your answers in both fraction AND percentage form for credit):

a) The probability of getting all heads?
b) The probability of getting heads first?
c) The probability of getting at least 1 tails?
d) The probability of getting 1 heads and 2 tails?
e) The probability of not getting any heads?

7) Write out the sample space for rolling 2 standard dice?

8) Find the following probabilities when rolling a standard dice two times (write your answers in both fraction AND percentage form for credit):

a) The probability of getting doubles (the same result on each die)?
b) The probability of getting a sum of 7 on the two dice?
c) The probability of getting a sum of 7 or 11 on the two dice?
d) The probability of getting at least one even number?
e) The probability of not rolling any 5’s?
f) The probability that the first die roll is a smaller number than the second die roll?
g) The probability that the second die roll is a 6?

9) Consider a jar containing 6 blue marbles, 8 red marbles, and 5 green marbles.  You pick one marble from the jar.

a) What is the probability of picking a blue marble?
b) What is the probability of picking a blue or a green marble?
c) What is the probability of picking a blue and a green marble?
d) What is the probability of not picking a red marble?

10) Consider a jar containing 6 blue marbles, 8 red marbles, and 5 green marbles.  You pick one marble from the jar, then put it back in the jar.  Then you draw a second marble. (This is selection with replacement)

a) What is the probability that both selections are red?
b) What is the probability that you pick a red marble followed by a green marble?
c) What is the probability that you pick a red and a green marble?
d) What is the probability of not picking a green marble?

11) Consider a jar containing 6 blue marbles, 8 red marbles, and 5 green marbles.  You pick one marble from the jar and set it aside.  Then you draw a second marble. (This is selection without replacement)

a) What is the probability that both selections are red?
b) What is the probability that you pick a red marble followed by a green marble?
c) What is the probability that you pick a red and a green marble?
d) What is the probability of not picking a green marble?

For the following questions, consider a complete deck of playing cards with no jokers.  If you are not familiar with cards, I’ve put an image of each of the 52 cards in a deck at the end of this assignment for your reference.

12) Find the following probabilities of drawing a single card from the deck:

a) Picking a 10?
b) Picking the Queen of hearts?
c) Picking a Diamond or a 3?
d) Picking a red card?
e) Picking a black Ace?
f) Not picking a black Ace?

13) Find the following probabilities of drawing two cards from the deck (without replacement):

a) Picking two number cards?
b) Picking two Jacks?
c) Picking two red cards?
d) Picking a Queen followed by a King?
e) Picking a Queen and a King?

14)  In the 2020 election, 66.8% of citizens aged 18 and older voted.

a) If you randomly talk to 3 citizens, what is the probability that all 3 of them voted in the 2020 election?
b) If you randomly talk to 3 citizens, what is the probability that none of them voted in the 2020 election?
c) If you randomly talk to 3 citizens, what is the probability that at least 1 of them voted in the 2020 election?
d) If you randomly talk to 3 citizens, what is the probability that exactly 1 person voted in the 2020 election?

15) During the pandemic, 78% of pet owners acquired a new pet.

a) If you randomly talk to 4 pet owners, what is the probability that all 4 of them got new pets during the pandemic?
b) If you randomly talk to 4 pet owners, what is the probability that none of them got new pets during the pandemic?
c) If you randomly talk to 4 pet owners, what is the probability that at least one of them got new pets during the pandemic?