Question

A letter is selected at random from the alphabet. What is the probability that it is one of the letters in the word “probability?” What is the probability that it occurs in the first half of the alphabet? What is the probability that it is a letter after x?

Short answer

The probability that the selected letter is one of the letters in the word “probability” is 9/26.

The probability that the selected letter occurs in the first half of the alphabet is 1/2.

The probability that the selected letter occurs after x is 1/13.

Step-by-step solution

Definition of favorable outcomes in probability

The number of times a particular event from the total number of events is expected to occur is defined as the favorable outcome. For instance, occurrence of 2 on die, then 2 is the only favorable outcome out of 6 numbers on die.

Determination of the probability that the selected letter is one of the letters in the word “probability”

There are 26 letters in the alphabets, this implies that for selecting a letter there are 26 total possible outcomes.

There is total 9 different letters in the word “probability” namely (p, r, o, b, a, i, l, t, y), this implies that the number of outcomes favourable are 9.

Write the expression for the probability.

P = number of outcomes favorable to E/total number of outcomes

Substitute the values in the above expression to find the probability that the selected letter is one of the letters in the word “probability”

P = 9/26

Determination of the probability that the selected letter occurs in the first half of the alphabet

The first half of the alphabet series has 13 letters, this implies that the number of outcomes favorable are 13 and total number of outcomes are 26.

Substitute the values in the equation (i) to find the probability that the selected letter occurs in the first half of the alphabet.

P = 13/26

= 1/2

Determination of the probability that the selected letter occurs after x

It can be observed that there are only 2 letters after “x” namely “y” and “z”, this implies that the number of outcomes favorable are 2 and total number of outcomes are 26.

Substitute the values in the equation (i) to find the probability that the selected letter occurs after x.

P = 2/26

= 1/13

Thus, the probability that the selected letter is one of the letters in the word “probability” is 9/26, the probability that the selected letter occurs in the first half of the alphabet is 1/2, and the probability that the selected letter occurs after x is 1/13.