Following are three sets of letters. Draw one letter from Set 1 and place it in Set 2. Then draw one
letter from Set 2 and place it in Set 3. Finally, draw a letter from Set 3. What is the probability that
the last letter drawn is a B?
B C B B B B
Set 1 Set 2 Set 3
To find the probability that the last letter drawn is a B, we first need to determine the total number of possible outcomes.
Set 1 contains one letter: B.
Set 2 contains six letters: C B B B B B.
Set 3 contains six letters: B B B B B B.
To calculate the total number of possible outcomes, we multiply the number of options in each set: 1 x 6 x 6 = 36.
Now, let's determine the number of favorable outcomes, which is the number of ways to draw a B as the last letter.
To draw a B as the last letter, there are two steps:
1. Draw a letter from Set 1 and place it in Set 2.
Since there is only one letter in Set 1 (B), we can only draw a B in this step.
2. Draw a letter from Set 2 and place it in Set 3.
Set 2 contains six letters (C B B B B B), so there are six possible options to draw from.
However, since we want to draw a B in this step, there are two favorable outcomes (B B) out of the six possible options.
So, the number of favorable outcomes is 1 x 2 = 2.
Finally, we can calculate the probability by dividing the number of favorable outcomes by the total number of possible outcomes:
Probability = Number of Favorable Outcomes / Total Number of Possible Outcomes
Probability = 2 / 36 = 1/18.
Therefore, the probability that the last letter drawn is a B is 1/18.