A computer randomly selects a letter from the alphabet.

1. How many different outcomes are in the sample space?

2. What is the probability the computer produces the first letter of your first name?

1) 26 different outcomes are in the sample space.

2) 1 / 26 is the probability that the computer produces the first letter of your first name.

Step-by-step explanation:

1) You have to find out the different outcomes in the sample space:

A "Sample space" is defined as the set of all the possible outcomes of an event. Here, the given event is randomly selecting a letter from the alphabets.

Therefore, the sample space must contain all the possible alphabets that can be chosen randomly.

The sample space is the set of all the 26 alphabets in English language.

⇒ Sample space = {A, B, C, D ..., Y, Z}

⇒ 26 different outcomes.

2) The probability the computer produces the first letter of your first name:

Here, the required outcome is getting the first letter of your first name.

Probability = No. of required outcomes / total no. of outcomes.

For example, The name Alex Davis has the first letter of the fist name as alphabet 'A'.

∴ Probability = 1 / 26

Similarly, for any first name there is going to be any one alphabet from the 26 alphabets, thus the probability to get the first letter will be always 1 / 26.