Krishna puts the letters of the word SCHOOL on pieces of paper and puts the pieces in a bag. He draws two letters without looking. The first piece of paper is NOT REPLACED before the second piece is drawn. What is the probability that Krishna draws an O twice?

Question

show all your work
A 1/15
B 2/15
C 1/36
D1/18

Answer 1

First, let's determine the total number of ways Krishna can draw two letters from SCHOOL without replacement.

There are 6 letters in the word SCHOOL, so there are 6 ways to choose the first letter and 5 ways to choose the second letter (since the first letter isn't replaced). Therefore, the total number of ways to draw 2 letters is 6 x 5 = 30.

Next, let's determine the number of ways Krishna can draw an O twice.

There are 2 O's in the word SCHOOL, so the number of ways to draw an O first is 2. Since the first piece of paper isn't replaced, there is only 1 O left for the second draw. Therefore, the number of ways Krishna can draw an O twice is 2 x 1 = 2.

Finally, we calculate the probability by dividing the number of ways to draw an O twice by the total number of ways to draw 2 letters:

Probability = Number of ways to draw an O twice / Total number of ways to draw 2 letters = 2 / 30 = 1 / 15

Therefore, the probability that Krishna draws an O twice is 1/15, which corresponds to option A.