Download How Likely Is It? Answer Key

How Likely Is It?
Answer Key
1.
A bubble-gum machine contains 25 gumballs. There are 12 green, 6 purple, 2 orange, and 5 yellow
gumballs.
a. Find each theoretical probability.
P(green) =
P(purple) =
P(orange) =
P(yellow) = b. Find the sum.
P(green) + P(purple) + P(orange) + P(yellow) =
1
c. Write each of the probabilities in part (a) as a percent.
P(green) = 48%
P(purple) = 24%
P(orange) = 8%
P(yellow) = 20%
d. What is the sum of all the probabilities as a percent?
48 + 24 + 8 + 20 = 100%
e. What do you think the sum of the probabilities for all the possible outcomes must be for any situation?
1 or 100%
2.
Melissa is designing a birthday card for her sister. She has a blue, yellow, pink, and green sheet of
paper. She also has a black, red, and purple marker. Suppose Melissa chooses one sheet of paper and
one marker at random.
a. Make a tree diagram to find all the possible color
combinations.
b. What is the probability that Melissa chooses pink paper
and a red marker?
P(pink paper and red marker) = c. What is the probability she chooses blue paper? What is
the probability she doesn’t choose blue paper?
P(blue paper) = , P(not blue paper) = d. What is the probability that she chooses a purple
marker?
P(purple marker) = 3.
A bucket contains 24 blocks. Some are blue, some are green, some are red, and some are yellow. The
theoretical probabilities of drawing a blue, green, or red block are:
a. How many blue blocks are in the bucket?
24 = 2 blue blocks
b. How many green blocks are in the bucket?
24 = 3 green blocks
c. How many red blocks are in the bucket?
24 = 8 red blocks
d. How many yellow blocks are in the bucket?
24 – 2 – 3 – 8 = 11 yellow blocks
e. What is the probability of drawing a yellow block? What about not drawing a yellow block?
P(yellow block) = , P(not yellow block) = 4.
A science club hosts a carnival to raise money. A game called Making Purple at the carnival involves
using both of the spinners shown. If the player gets red on spinner A and blue on spinner B, the player
wins because mixing red and blue makes purple.
a. List the outcomes that are possible when you spin both pointers. Are the outcomes equally likely?
Explain your reasoning.
yellow-blue, yellow-orange, yellow-yellow, red-blue, red-orange, red-yellow, green-blue, greenorange, green-yellow
b. What is the theoretical probability that a player “makes purple”?
P(purple) = c. If 100 people play the Making Purple game, how many people do you expect to win?
100 11 people
5.
A box contains 12 slips of paper as shown. Each slip of paper is equally likely to be drawn.
Find each probability.
a. P(red) = b. P(blue) = c. P(red) + P(blue) = d. P(red or blue) = e. P(not red) = f. P(not blue) = 6.
A foot arch is a genetic trait. A foot arch is a space between the middle of a person’s foot and the floor
when the person stands. In a national study, 982 people said they had a foot arch, while 445 people
said they did not have a foot arch.
a. Based on these data, what is the experimental probability that a person chosen at random has a foot
arch?
P(foot arch) = 68.8%
b. In a recent year, about 16,600 people participatied in the Boston Marathon. Use the data above to
estimate the number of participants who did not have a foot arch.
31.2% of 16,600 = 0.312(16,600) ≈ 5179 people without a foot arch
7.
Assuming that it is equally likely for a person to be born a boy or a girl, answer the following questions.
a. What are all the possible outcomes of having two children? List the outcomes in the form:
(gender of first child, gender of second child)
(boy, boy), (boy, girl), (girl, girl), (girl, boy)
b. What is the probability that both children are girls?
P(girl, girl) = c. What is the probability that one child is a boy and the other is a girl?
P(boy and girl) = d. What is the probability that the first child is a boy?
P(boy first) =