MATH 225N WEEK 4 HOMEWORK PROBABILITY QUESTION
AND ANSWERS
1. Which of the pairs of events below is dependent?
Select the correct answer below:
drawing a 7 and then drawing another 7 with replacement from a standard deck of cards
rolling a 1 and then rolling a 6 with a standard die
rolling a 3 and then rolling a 4 with a standard die
drawing a heart and then drawing a spade without replacement from a standard deck of cards
2. Identify the option below that represents dependent events.
Select the correct answer below:
drawing a face card and then drawing a 3 without replacement from a standard deck of cards
rolling a sum of 6 from the first two rolls of a standard die and a sum of 4 from the second two rolls
drawing a 2 and drawing a 4 with replacement from a standard deck of cards
drawing a heart and drawing another heart with replacement from a standard deck of cards
3. Which of the following shows mutually exclusive events?
Select the correct answer below:
rolling a sum of 9 from two rolls of a standard die and rolling 2 for the first roll
drawing a red card and then drawing a black card with replacement from a standard deck of cards
drawing a jack and then drawing a 7 without replacement from a standard deck of cards
drawing a 7 and then drawing another 7 with replacement from a standard deck of cards
4. Which of the pairs of events below is mutually exclusive?
Select the correct answer below:
drawing an ace of spades and then drawing another ace of spades without replacement from a standard
deck of cards
drawing a 2 and drawing a 4 with replacement from a standard deck of cards
, drawing a heart and then drawing a spade without replacement from a standard deck of cards
drawing a jack and then drawing a 7 without replacement from a standard deck of cards
(Mutually exclusive events are events that cannot occur together. In this case, drawing an ace of spades and then
drawing another ace of spades without replacement from a standard deck of cards are two events that cannot possibly
occur together.)
5. A deck of cards contains RED cards numbered 1,2,3,4,5,6, BLUE cards
numbered 1,2,3,4,5, and GREEN cards numbered 1,2,3,4. If a single card is picked at
random, what is the probability that the card has an ODD number?
Select the correct answer below:
10/15
8/15
14/15
6/15
(By counting, we can see that there are 8 odd cards, and a total of 15 cards in the deck. So the probability is 8/15).
6. Hector is a baseball fan but wants to watch something different. There are 5 basketball
games, 2 football games, and 4hockey games that he can choose to watch. If Hector
randomly chooses a game, what is the probability that it is a basketball game?
Give your answer as a fraction.
Provide your answer below: 5/11
7. There are 26 cards in a hat, each of them containing a different letter of the alphabet. If one
card is chosen at random, what is the probability that it is not between the letters L and P,
inclusive?
Provide your answer below: 21/26
8. A spinner contains the numbers 1 through 80. What is the probability that the spinner will
land on a number that is not a multiple of 12?
Give your answer in fraction form.
Provide your answer below: 74/80
, 9. An art collector wants to purchase a new piece of art. She is interested in 5 paintings, 6 vases,
and 2 statues. If she chooses the piece at random, what is the probability that she selects a
painting?
Give your answer as a fraction.
Provide your answer below: 5/13
10. Boris is taking a quiz for an online class. For the quiz, the system randomly assigns 2 high-
difficulty questions, 7 moderate-difficulty questions, and 6 low-difficulty questions. What is
the probability that Boris is assigned a moderate-difficulty question first?
Give your answer as a fraction.
Provide your answer below: 7/15
11. A spinner contains the numbers 1 through 40. What is the probability that the spinner will
land on a number that is not a multiple of 6? Give your answer as a fraction.
Provide your answer below: 34/40
12. A spinner contains the numbers 1 through 50. What is the probability that the spinner will
land on a number that is not a multiple of 4?
Provide your answer below: 38/50
13. Identify the parameters p and n in the following binomial distribution scenario. The probability
of winning an arcade game is 0.718 and the probability of losing is 0.282. If you play the
arcade game 20 times, we want to know the probability of winning more than 15 times.
(Consider winning as a success in the binomial distribution.)
p=0.282, n=20
p=0.718, n=15
p=0.718, n=20
p=0.282, n=15
(The parameters p and n represent the probability of success on any given trial and the total number of trials,
respectively. In this case, success is winning a game, so p=0.718. The total number of trials, or games,
is n=20)
AND ANSWERS
1. Which of the pairs of events below is dependent?
Select the correct answer below:
drawing a 7 and then drawing another 7 with replacement from a standard deck of cards
rolling a 1 and then rolling a 6 with a standard die
rolling a 3 and then rolling a 4 with a standard die
drawing a heart and then drawing a spade without replacement from a standard deck of cards
2. Identify the option below that represents dependent events.
Select the correct answer below:
drawing a face card and then drawing a 3 without replacement from a standard deck of cards
rolling a sum of 6 from the first two rolls of a standard die and a sum of 4 from the second two rolls
drawing a 2 and drawing a 4 with replacement from a standard deck of cards
drawing a heart and drawing another heart with replacement from a standard deck of cards
3. Which of the following shows mutually exclusive events?
Select the correct answer below:
rolling a sum of 9 from two rolls of a standard die and rolling 2 for the first roll
drawing a red card and then drawing a black card with replacement from a standard deck of cards
drawing a jack and then drawing a 7 without replacement from a standard deck of cards
drawing a 7 and then drawing another 7 with replacement from a standard deck of cards
4. Which of the pairs of events below is mutually exclusive?
Select the correct answer below:
drawing an ace of spades and then drawing another ace of spades without replacement from a standard
deck of cards
drawing a 2 and drawing a 4 with replacement from a standard deck of cards
, drawing a heart and then drawing a spade without replacement from a standard deck of cards
drawing a jack and then drawing a 7 without replacement from a standard deck of cards
(Mutually exclusive events are events that cannot occur together. In this case, drawing an ace of spades and then
drawing another ace of spades without replacement from a standard deck of cards are two events that cannot possibly
occur together.)
5. A deck of cards contains RED cards numbered 1,2,3,4,5,6, BLUE cards
numbered 1,2,3,4,5, and GREEN cards numbered 1,2,3,4. If a single card is picked at
random, what is the probability that the card has an ODD number?
Select the correct answer below:
10/15
8/15
14/15
6/15
(By counting, we can see that there are 8 odd cards, and a total of 15 cards in the deck. So the probability is 8/15).
6. Hector is a baseball fan but wants to watch something different. There are 5 basketball
games, 2 football games, and 4hockey games that he can choose to watch. If Hector
randomly chooses a game, what is the probability that it is a basketball game?
Give your answer as a fraction.
Provide your answer below: 5/11
7. There are 26 cards in a hat, each of them containing a different letter of the alphabet. If one
card is chosen at random, what is the probability that it is not between the letters L and P,
inclusive?
Provide your answer below: 21/26
8. A spinner contains the numbers 1 through 80. What is the probability that the spinner will
land on a number that is not a multiple of 12?
Give your answer in fraction form.
Provide your answer below: 74/80
, 9. An art collector wants to purchase a new piece of art. She is interested in 5 paintings, 6 vases,
and 2 statues. If she chooses the piece at random, what is the probability that she selects a
painting?
Give your answer as a fraction.
Provide your answer below: 5/13
10. Boris is taking a quiz for an online class. For the quiz, the system randomly assigns 2 high-
difficulty questions, 7 moderate-difficulty questions, and 6 low-difficulty questions. What is
the probability that Boris is assigned a moderate-difficulty question first?
Give your answer as a fraction.
Provide your answer below: 7/15
11. A spinner contains the numbers 1 through 40. What is the probability that the spinner will
land on a number that is not a multiple of 6? Give your answer as a fraction.
Provide your answer below: 34/40
12. A spinner contains the numbers 1 through 50. What is the probability that the spinner will
land on a number that is not a multiple of 4?
Provide your answer below: 38/50
13. Identify the parameters p and n in the following binomial distribution scenario. The probability
of winning an arcade game is 0.718 and the probability of losing is 0.282. If you play the
arcade game 20 times, we want to know the probability of winning more than 15 times.
(Consider winning as a success in the binomial distribution.)
p=0.282, n=20
p=0.718, n=15
p=0.718, n=20
p=0.282, n=15
(The parameters p and n represent the probability of success on any given trial and the total number of trials,
respectively. In this case, success is winning a game, so p=0.718. The total number of trials, or games,
is n=20)
