Question

Charlie has a piece of toast that has cream cheese on one side, and he dropped it once. One time, it landed with the cream cheese side up. If he drops it two more times, what is the probability that it will have landed cream cheese side up a total of three times?
one over four
one over three
one over eight
three over four

Answer 1

Answer: first option, 1/4.

Explanation:

1) Every drop is an independent event. So, the joint probability is the product of the individual probabilities.

2) The fact that the piece ot toast landed once time with the cream cheese side up, does not affect the next two drops.

3) Since, the piece of toast landed the first time with cream cheese side up, the probability that it it will have landed cream cheese side up a total of three times is the probability that it will have landed two more times with cream cheese side up.

3) The probability that the piece of toast will have landed cream cheese side up two more times is 1/2 × 1/2 = 1/4. And that is the answer to the question.

Answer 2

Just multiply the probability of each instance together (in fraction form). 1/2 * 1/2 * 1/2 = 1/8.
However, be aware that this only works because it asked what the probability of it happening three times in a row. For example, if the question read, "What is the probability of this piece of bread landing butter side down, assuming it has already landed three times butter side down?", the answer would be 1/2 because the probability of previous incidents do not actually physically affect a future test.