# Lesson 9

Using Tables for Conditional Probability

### 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.

### Solution

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### 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?

### Solution

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### 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?

\(\frac{25}{30}\)

\(\frac{14}{30}\)

\(\frac{14}{25}\)

\(\frac{14}{17}\)

### Solution

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### 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?

\(\frac{1}{2}\)

\(\frac{1}{6}\)

\(\frac{1}{12}\)

\(\frac{3}{12}\)

### Solution

### 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?

### Solution

### 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.

### Solution

### 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?

### Solution

### 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.

### Solution

### 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?