3.4 Contingency Tables and Probability Trees

Calculate the following probabilities using the table.

1. Find P(Driver is a cell phone user).
2. Find P(Driver had no violation in the last year).
3. Find P(Driver had no violation in the last year $\cap$ was a cell phone user).
4. Find P(Driver is a cell phone user $\cup$ driver had no violation in the last year).
5. Find P(Driver is a cell phone user $\left|\right.$ driver had a violation in the last year).
6. Find P(Driver had no vio…

the table shows the number of athletes who stretch before exercising and how many had injuries within the past year.

1. What is P(athlete stretches before exercising)?
2. What is P(athlete stretches before exercising$\left|\right.$no injury in the last year)?

a. Complete the table.

b. Are the events "being a woman" and "preferring the coastline" independent events?

Let F = being a woman and let C = preferring the coastline.

1. Find $P \left(F \cap C\right)$.
2. Find P(F)P(C)

Are these two numbers the same? If they are, then F and C are independent. If they are not, then F and C are not independent.

c. Find the probability that a person is a man given that the person prefers hiking near lakes and streams. Let M = being a man, and let L = prefers hiking near lakes and streams.

1. What word tells you this is a conditional?
2. Fill in the blanks and calculate the probability: P(___$\left|\right.$___) = ___.
3. Is the sample space for this problem all 100 hikers? If not, what is it?

d. Find the probability that a person is a woman or prefers hiking on mountain peaks. Let F = being a woman, and let P = prefers mountain peaks.

1. Find P(F).
2. Find P(P).
3. Find $P \left(F \cap P\right)$.
4. Find $P \left(F \cup P\right)$.

the table shows a random sample of 200 cyclists and the routes they prefer. Let O = older and H = hilly path.

1. Out of the older group, what is the probability that the cyclist prefers a hilly path?
2. Are the events “being older” and “preferring the hilly path” independent events?

Verify the remaining entries.

a. Complete the probability contingency table. Calculate the entries for the totals. Verify that the lower-right corner entry is 1.

Verify the remaining entries.

b. What is the probability that Alissa does not catch Muddy?

Verify the remaining entries.

c. What is the probability that Muddy chooses Door One $\cup$ Door Two given that Muddy is caught by Alissa?

Fred's preference to drink coffee or iced tea depends on the season. When it is summer, Fred's preference to drink coffee is $\frac{1}{4} ,$ and his preference to drink iced tea is $\frac{3}{4} .$When it is rainy season, Fred's preference to drink coffee is $\frac{1}{2} ,$and his preference to drink iced tea is $\frac{1}{2} .$ When it is winter, Fred's preference to drink coffee is $\frac{1}{5} ,$ and his preference to drink iced tea is $\frac{1}{5} .$ A day randomly selected in…

TOTAL each column and each row. Total data = 4,520.7

1. Find P(Year 2 AND Robbery).
2. Find P(Year 3 AND Burglary).
3. Find P(Year 3 OR Burglary).
4. Find P(Year 4 | Vandalism).
5. Find P(Vehicle | Year 1).

the table relates the weights and heights of a group of individuals participating in an observational study.

1. Find the total for each row and column
2. Find the probability that a randomly chosen individual from this group is Tall.
3. Find the probability that a randomly chosen individual from this group is Overweight and Tall.
4. Find the probability that a randomly chosen individual from this group is Tal…

There are a total of 11 balls in the urn. Draw two balls, one at a time, with replacement. There are 11(11) = 121 outcomes, the size of the sample space.

a. List the 24 BR outcomes: B1R1, B1R2, B1R3, ...

There are a total of 11 balls in the urn. Draw two balls, one at a time, with replacement. There are 11(11) = 121 outcomes, the size of the sample space.

b. Using the tree diagram, calculate P(RR).

There are a total of 11 balls in the urn. Draw two balls, one at a time, with replacement. There are 11(11) = 121 outcomes, the size of the sample space.

c. Using the tree diagram, calculate $P \left(RB \cup BR\right)$.

There are a total of 11 balls in the urn. Draw two balls, one at a time, with replacement. There are 11(11) = 121 outcomes, the size of the sample space.

d. Using the tree diagram, calculate $P \left(R \text{on 1st draw} \cap B \text{on 2nd draw}\right)$.

There are a total of 11 balls in the urn. Draw two balls, one at a time, with replacement. There are 11(11) = 121 outcomes, the size of the sample space.

e. Using the tree diagram, calculate P(R on 2nd draw$\left|\right.$B on 1st draw).

There are a total of 11 balls in the urn. Draw two balls, one at a time, with replacement. There are 11(11) = 121 outcomes, the size of the sample space.

f. Using the tree diagram, calculate P(BB).

There are a total of 11 balls in the urn. Draw two balls, one at a time, with replacement. There are 11(11) = 121 outcomes, the size of the sample space.

g. Using the tree diagram, calculate P(B on the 2nd draw$\left|\right.$R on the first draw).

Calculate the following probabilities using the tree diagram.

a. P(RR) = ________

Calculate the following probabilities using the tree diagram.

b. Fill in the blanks:

$P \left(RB \cup BR\right)$ = $\left(\frac{3}{11}\right) \left(\frac{8}{10}\right) \textrm{ } + \textrm{ }(___)(___)\textrm{ } = \textrm{ } \frac{48}{110}$

Calculate the following probabilities using the tree diagram.

c. P(R on 2nd$\left|\right.$B on 1st) =

Calculate the following probabilities using the tree diagram.

d. Fill in the blanks.

$P \left(R \text{on 1st} \cap B \text{on 2nd}\right)$ = (___)(___) = $\frac{24}{110}$

Calculate the following probabilities using the tree diagram.

e. Find P(BB).

Calculate the following probabilities using the tree diagram.

f. Find P(B on 2nd$\left|\right.$R on 1st).

Suppose there are four red balls and three yellow balls in a box. Two balls are drawn from the box without replacement. What is the probability that one ball of each coloring is selected?