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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.

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P(A then B then A)

1 answer

To calculate the probability of the outcome P(A then B then A) in this scenario, we look for the specific combination of letters being selected in that order (A, then B, then A).

Let's list the total outcomes based on your table:

  1. A A A
  2. A A B
  3. A B A
  4. B A A
  5. B B A
  6. A B B
  7. B A B
  8. B B B

The only instance of A followed by B followed by A (A, B, A) appears once:

  • A B A

Thus, the probability P(A then B then A) can be calculated using the following formula:

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

By matching the value to the probability statement:

  • The value for P(A then B then A) is \( \frac{1}{8} \).