Question

Question 3 2 pts a.) List the sample space for selecting a letter at random from the word "PINEAPPLE". Separate your letters with a comma and do not include spaces. b.) A letter is randomly selected from the word "PINEAPPLE". Which is more likely, selecting "E" or selecting "P"?

Answer 1

a. The sample space, S, is the set of possible outcomes of a random experiment.

Let the experiment be "select a letter at random from the word pineapple" each word will represent possible outcomes of the sample space to that:

The word has a total of 9 letters, which are:

3 P

2 E

1 I

1 A

1 N

The sample space can be defined as:

`S=\mleft\lbrace A,E,I,N,P\mright\rbrace`

(Note: I ordered the sample space alphabetically)

b. You have to determine which event has the highest probability, selecting letter at random and the result being an E or a P. Before you can compare the probabilities of both letters, you have to calculate them:

To determine the said individual probabilities, you have to calculate the quotient between the number of favorable cases and the number of total cases.

For the event "selecting a word at random and the letter is E"

- The total number of cases is 9 (number of letters on the word pineapple)

- The number of favorable cases is 2 (times the letter E is in the word pineapple)

`P(E)=(2)/(9)=0.22`

For the event "selecting a word at random and the letter is P"

- The total number of cases is 9 (number of letters on the word pineapple)

- The number of favorable cases is 3 (times the letter P is in the word pineapple)

`P(P)=(3)/(9)=(1)/(3)\approx0.33`

The probability of selecting the letter "E" is 0.22 while the probability of selecting the letter "P" is 0.33.

Then selecting the letter "P" is more likely than selecting the letter "E"