Lesson 9
Using Tables for Conditional Probability
- Let’s use tables to estimate conditional probabilities.
Problem 1
A tour company makes trips to see dolphins in the morning and in the afternoon. The two-way table summarizes whether or not customers saw dolphins on a total of 40 different trips.
| morning | afternoon | |
|---|---|---|
| dolphins | 19 | 14 |
| no dolphins | 3 | 4 |
- If a trip is selected at random, what is the probability that customers did not see dolphins on that trip?
- If a trip is selected at random, what is the probability that customers did not see dolphins under the condition that the trip was in the morning?
- Are the events of seeing dolphins and the time of the trip (morning or afternoon) dependent or independent events? Explain your reasoning.
Problem 2
Noah is unsure whether the coin and number cube he has are fair. He flips the coin then rolls the number cube and records the result. He does this a total of 50 times. The results are summarized in the table.
| one | two | three | four | five | six | |
|---|---|---|---|---|---|---|
| heads | 5 | 3 | 5 | 3 | 5 | 6 |
| tails | 3 | 4 | 5 | 2 | 6 | 3 |
- Create a two-way table that displays the probability for each outcome based on Noah’s tests.
- If one of Noah’s 50 results is selected at random, what is the probability that the coin was heads?
- If one of Noah’s 50 results is selected at random, what is the probability that the number cube was 5?
Problem 3
A student surveys 30 people as part of a project for a statistics class. Here are the survey questions.
- Are you left-handed or right-handed?
- Are you left-eye dominant or right-eye dominant?
The results of the survey are summarized in the two-way table.
| right-eye dominant | left-eye dominant | |
|---|---|---|
| right-handed | 14 | 11 |
| left-handed | 3 | 2 |
What is the probability that a person from the survey chosen at random is right-handed under the condition that they are right-eye dominant?
\(\frac{25}{30}\)
\(\frac{14}{30}\)
\(\frac{14}{25}\)
\(\frac{14}{17}\)
Problem 4
Priya flips a fair coin and then rolls a standard number cube. What is the probability that she rolled a 3 under the condition that she flipped heads?
\(\frac{1}{2}\)
\(\frac{1}{6}\)
\(\frac{1}{12}\)
\(\frac{3}{12}\)
Problem 5
Andre flips one fair coin and then flips another fair coin.
- What is the probability that he gets heads on both coins?
- What is the probability that he gets heads on the second coin under the condition that the first flip is heads?
- What is the probability that the second flip is not heads?
- What is the probability that the first flip is heads and the second flip is not heads?
Problem 6
Han randomly selects a card from a standard deck of cards. He places it on his desk and then Jada randomly selects a card from the remaining cards in the same deck.
- What is the probability that Han selects a card that has diamonds on it?
- What is the probability that Jada selects a card that has diamonds on it?
- What is the probability that Han selects a card that has diamonds on it and that Jada selects a card that has diamonds on it?
- Are the events of Han and Jada randomly selecting a card dependent or independent? Explain your reasoning.
Problem 7
An agriculturist takes 50 samples of soil and measures the levels of two nutrients, nitrogen and phosphorus. In 46% of the samples the nitrogen levels are low and in 28% of the samples the phosphorus levels are low. In 10% of the samples both the nitrogen and the phosphorus levels are low. What percentage of the samples have nitrogen levels or phosphorus levels that are low?
Problem 8
Select all of the situations that have a 50% chance of occurring.
Rolling a standard number cube and getting a 3.
Flipping two fair coins and getting heads on exactly one of the flips.
Picking a letter at random from the word SEED and getting an E.
Picking a letter at random from the word ORCHID and getting a vowel.
Getting the answer correct when guessing randomly on a true or false question.
Problem 9
A solid has volume 6 cubic units and surface area 14 square units. The solid is dilated, and the image has surface area 224 square units. What is the volume of the image?