Contemporary Mathematics

# Chapter Test

### 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 with 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?
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