Lesson 5 I Will Survive! Solidify Understanding

Ready

Find the products or quotients below.

1.

$\frac{1}{2} \cdot \frac{2}{3}$

2.

$\frac{3}{5} \cdot \frac{1}{3}$

3.

$\frac{7}{10} \cdot \frac{2}{5}$

4.

$\frac{8}{7} \cdot \frac{3}{4}$

5.

$\frac{\frac{1}{3}}{\frac{1}{2}}$

6.

$\frac{2}{5} \div \frac{2}{3}$

7.

$P (A) = \frac{3}{4}$ , $P (B) = \frac{1}{2}$

$P (A) \cdot P (B) =$

8.

$P (A) = \frac{1}{6}$ , $P (B) = \frac{1}{3}$

$P (A) \cdot P (B) =$

Set

For each situation, one of the representations (two-way table, Venn diagram, tree diagram, context, or probability notation) is provided. Use the information to complete the remaining representations.

9.

Researchers surveyed residents of both the Northern and Southern Hemispheres. The residents were asked if they lived on the coast or inland. The results are provided.

Notation	Two-way Table
Key: $Northern = N$ $Southern = S$ $On Coast = C$ $Inland = I$ $Sample size = 200$ $P (C) = \frac{84}{200}$ $P (N) = \frac{64}{200}$ $P (S \| C) = \frac{48}{84}$ $P (C \| S) =$ $P (N \cap C) =$ $P (N or C) =$

Notation

Two-way Table

Key:

$Northern = N$

$Southern = S$

$On Coast = C$

$Inland = I$

$Sample size = 200$

$P (C) = \frac{84}{200}$

$P (N) = \frac{64}{200}$

$P (S | C) = \frac{48}{84}$

$P (C | S) =$

$P (N \cap C) =$

$P (N or C) =$

Venn diagram	Tree Diagram

Write three observations you can make about this data:

10.

A group of people were asked if they were left-handed or right-handed and whether they like vegetables.

Notation	Two-way Table
Key: $Like Vegetables = V$ $Don’t Like Vegetables = D$ $Lefty = L$ $Righty = R$ $Sample size = 100 people$ $P (L) =$ $P (V) =$ $P (D) =$ $P (L \| D) =$ $P (L \| V) =$

Notation

Two-way Table

Key:

$Like Vegetables = V$

$Don’t Like Vegetables = D$

$Lefty = L$

$Righty = R$

$Sample size = 100 people$

$P (L) =$

$P (V) =$

$P (D) =$

$P (L | D) =$

$P (L | V) =$

Venn diagram	Tree Diagram

Write three conditional probability statements regarding this data:

11.

A sample of people were asked if they drink cola drinks or not and if they eat breakfast or not.

Notation	Two-way Table
Key: $Cola Drinkers = C$ $No Cola Drinks = N$ $Eats Breakfast = E$ $Doesn’t Eat Breakfast = D$ $Sample size =$ $P (E) =$ $P (E \| C) =$ $P (E \cap C) =$ $P (E \| N) =$ $P (E \cap N) =$

Notation

Two-way Table

Key:

$Cola Drinkers = C$

$No Cola Drinks = N$

$Eats Breakfast = E$

$Doesn’t Eat Breakfast = D$

$Sample size =$

$P (E) =$

$P (E | C) =$

$P (E \cap C) =$

$P (E | N) =$

$P (E \cap N) =$

Venn diagram	Tree Diagram

Does this data surprise you? Why or why not?

Go

12.

Complete the table and find the conditional probabilities, then interpret the data and probabilities to respond to the problem.

	Biking	Swimming	Total
10th Grade		$50$
11th Grade	$35$		$76$
Total	$85$

$P (10 th | Biking) =$

$P (Swimming | 11 th) =$

Are the $11 th$ grade students more into biking or swimming?

13.

Complete the table about the dessert preference of teens and adults. Find the conditional probabilities, then interpret the data and probabilities to respond to the problem.

	Ice Cream	Cake	Total
Teen		$20$
Adult	$10$		$60$
Total	$85$

$P (Teen | Cake) =$

$P (Adult or Ice Cream) =$

Who prefers eating ice cream most, adults or teens?

14.

Fill in the missing values for the frequency table containing data from a sample of adults. The table shows voting turnout and household income for a recent election. Find the indicated probabilities, then interpret the data and probabilities to respond to the problem.

	Voted	Total
Income Over $$ 67,500$	$340$	$410$
Income Under $$ 67,500$
Total	$584$	$840$

$P (Voted | Income Over $ 67,500) =$

$P (Voted and Income Under $ 67,500) =$

$P (Didn’t Vote or Income Under $ 67,500) =$

Based on the sample of data, are all income levels participating in the election equally?