Question

A die is rolled then a letter in the word STATISTICS is randomly selected. What is the probability of at least a 3 then the letter S?

Answer 1

Answer: Hello mate!

The event is "A die is rolled then a letter in the word STATISTICS is randomly selected."

first we need to see the probability of at least a 3 in the die.

the die has 6 sides, with numbers 1, 2, 3, 4, 5, and 6.

then there are 3 options that give a result of at least 3, then the probability is calculated as the quotient of these options and the total amount of options: this is 3/6 = 1/2.

Now let's find the probability of randomly chose the letter y from the word STATISTICS, in this word, there are a total of 10 letters, and 3 of them are S.

Then the probability of randomly select the letter S is equal to 3/10.

Now we want to know the joint probability of these two events, and this is obtained as the multiplication of their probabilities.

This is p = (1/2)*(3/10) = (3/20)

Then the probability of " rolling at least a 3 and then selecting the letter S" is equal to 3/20

that you can write as a percentage in the next way:

(3/20)*100% = 0.15*100% = 15%

Answer 2

The first answer for the die is 1/6 because there are six sides and one 3 on one die
for the second it is 3/10 because there are three S and there are ten letters in the word