1. The distribution of Scrabble tiles and their points are given below. As you might expect, there are more vowels and common consonants (e.g. R, T). High point tiles such as Q and Z occur less frequently. One game has 100 tiles total.
Letter |
Point Value |
Frequency |
A |
1 |
9 |
B |
3 |
2 |
C |
3 |
2 |
D |
2 |
4 |
E |
1 |
12 |
F |
4 |
2 |
G |
2 |
3 |
H |
4 |
2 |
I |
1 |
9 |
J |
8 |
1 |
K |
5 |
1 |
L |
1 |
4 |
M |
3 |
2 |
N |
1 |
6 |
O |
1 |
8 |
P |
3 |
2 |
Q |
10 |
1 |
R |
1 |
6 |
S |
1 |
4 |
T |
1 |
6 |
U |
1 |
4 |
V |
4 |
2 |
W |
4 |
2 |
X |
8 |
1 |
Y |
4 |
2 |
Z |
10 |
1 |
Blank |
0 |
2 |
Suppose we were to perform an experiment that consisted of drawing one tile from the bag. Let's define the random variable X as the number of points a tile is worth.
a. Explain why X would be considered a discrete random variable
b. What are the possible outcomes for the random variable X?
c. What is the probability that a randomly selected tile is worth 0 points? That is , find P(X=0).
d. What is the probability that a randomly selected tile is worth 4 points? That is , find P(X=4).
e. Similar to (c) and (d), find the proabability for all possible outcomes and list them in the table below.
This table is known as the probability distribution of X.
f. Using the table in (e), compute the probability that a tile is worth at most 3 points
g. compute the probability that a tile is worth at least 2 points.
h. find the expected (mean) number of points a Scrabble tile is worth.