Question

We have a fair die inscribed with the letters A through F. What's the probability of rolling the die three times and getting the first 3 letters of the alphabet? What's the probability of rolling one of the first three letters in 1 roll?

Answer 1

See below:

Explanation:

If I understand the question, we have a 6-sided fair die that instead of having the numbers 1-6, it has the letters A-F. What is the probability of rolling the first three letters of the alphabet?

In my reading of the question, it's a little ambiguous, so I'll answer in a couple of different ways.

3 rolls: 1st an A, then a B, last a C

The probability of rolling an A is `1/6`. In fact, the probability of rolling any given letter is `1/6`. And so we can roll the die 3 times and each time there is a `1/6` probability we'll get the correct letter of the alphabet:

`P("A, then B, then C")=1/6xx1/6xx1/6=1/6^3=1/216`

3 rolls: 1st one of the first 3 letters, 2nd on of the two remaining letters, 3rd the last letter

On the first roll, we can have either A, B, or C. And so the probability on the first roll of getting one of them is `3/6=1/2`

On the second roll, we're now looking to roll one of the remaining letters (let's say roll 1 we rolled C, so now we want either A or B). The probability on this roll is `2/6=1/3`.

On the third roll, there is one letter remaining and so that is `1/6`.

Putting it altogether then, we get:

`P("within 3 rolls get the first 3 letters of the alphabet")=1/2xx1/3xx1/6=1/36`

1 roll: rolling one of the first three letters of the alphabet

We saw this one above - the probability is `1/2`