Question

A six sided die has two sides numbered with a 1, three sides numbered with a 2, and one side that is blank (0).

Answer 1

There is a difference between the expected value and the value you get when you actually try this experiment

The value you would get if you actually tried the experiment

You would expect to get 3/6 for the 2. This means that when you throw the die any number of times, you will get a 2 about 1/2 the time. If you throw the die 1500 times 750 of them should be a 2.

You would expect to get 2/6 for the 1. When you throw the die any number of times, you would expect to get a "1" 1 out of 3 times. If you throw the die 3000 times, 1000 of them should be a 1.

You would expect to get 1/6 for the blank. This means that for any number of throws 1 out of every 6 should come up blank. In other words, if you divided the number of throws by 6, you should get that many blanks.

The actual value is as above

The expected value in probability is

2 * 1/2 = 1

1 * 1/3 = 0.3333

0 * 1/6 = 0

The expected value = 1.33 just as you said.