### Chapter Test

Each of the following exercises involve drawing a

*Scrabble*tile from a bag. These tiles are labeled with a letter and a point value, as follows: A(1), C(3), D(2), E(1), E(1), J(8), K(5), O(1), R(1), R(1).1
.

How many ways are there to draw a vowel and then a consonant from the bag?

2
.

How many ways are there to draw a tile worth an even number of points and then a tile worth an odd number of points from the bag?

3
.

How many ways are there to draw 4 tiles from the bag without replacement, if order matters?

4
.

How many ways are there to draw 4 consonants from the bag without replacement, if order matter?

5
.

How many ways are there to draw 4 tiles from the bag with replacement, if order does not matter?

6
.

How many ways are there to draw 4 consonants from the bag with replacement, if order does not matter?

7
.

Give the sample space of the experiment that asks you to draw 2 tiles from the bag with replacement and note their point values, where order doesn’t matter. Give the outcomes as ordered pairs.

8
.

Give the sample space of the experiment that asks you to draw 2 tiles from the bag without replacement and note their point values, where order doesn’t matter. Give the outcomes as ordered pairs.

9
.

If you draw a single tile from the bag, what is the probability that it’s an E?

10
.

If you draw a single tile from the bag, what is the probability that it’s

*not*an A?11
.

If you draw 3 tiles from the bag without replacement, what is the probability that they spell RED, in order?

12
.

If you draw 3 tiles from the bag without replacement, what is the probability that they spell RED, in

*any*order?13
.

What are the odds against drawing a vowel?

14
.

Use your answer to question 12 to find the odds against drawing three tiles without replacement and being able to spell RED.

15
.

If you draw one tile, what is the probability of drawing a J or a K?

16
.

If you draw one tile, what is the probability that it’s a vowel or that it’s worth more than 4 points?

17
.

Suppose you’re about to draw one tile from the bag. Find $P(\text{the letter is R})$ and $P(\text{the letter is R}|\text{the point value is 1})$.

18
.

If you draw 2 tiles with replacement, what is the probability of drawing a consonant first and then a vowel?

19
.

If you draw 2 tiles

*without*replacement, what is the probability of drawing a consonant first and then a vowel?20
.

If you draw 10 tiles with replacement, what is the probability that you draw exactly 3 vowels? Round to 3 decimal places.

21
.

If you draw 100 tiles with replacement, what is the probability that you draw fewer than 35 vowels? Round to 4 decimal places.

22
.

Find and interpret the expected number of points on the tile, assuming you draw 1 tile from the bag.

23
.

Find the expected sum of points on 2 tiles, selected without replacement.

24
.

If your friend offers you a bet where they pay you $10 if you draw a vowel from the bag, but you owe them $5 if you draw a consonant, should you take it? How do you know?