Question

A computer is used to pick three letters, one after the other, from {A, B}. Each letter can be picked more than once and has the same chance of being selected.

The possible outcomes for this experiment are given in this table.

A A A A A B A B A B A A
B B A A B B B A B B B B
Drag and drop to match the value to the probability statement.

Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
P(A then B then A)

0.125 0.250 0.375 0.500 0.625

Answer 1

To calculate the probability of the specific sequence P(A then B then A), we need to consider the total number of outcomes and the number of favorable outcomes for that specific sequence.

The total outcomes when picking three letters from the set {A, B} is \(2^3 = 8\). This is because each letter can be either A or B, giving us:

- AAA
- AAB
- ABA
- ABB
- BAA
- BAB
- BBA
- BBB

Now, we look for the specific sequence "A then B then A", which corresponds to the outcome ABA.

From our list of outcomes, there is only 1 outcome that matches ABA.

To find the probability:

\[
P(A \text{ then } B \text{ then } A) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{1}{8} = 0.125
\]

So, the answer to the probability statement P(A then B then A) is:

**0.125**