Question

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

The possible outcomes for this experiment are shown in the table.

AA BA CA
AB BB CB
AC BC CC
Drag and drop to match the value to the probability statement. Note decimals have been rounded to the hundredths place.
P(AA or BB)

0.11 0.22 0.33 0.44 0.55

Answer 1

There are two desired outcomes we want. Those outcomes are AA and BB. If we get either of them, then we achieve the goal. This is out of 9 outcomes total. Divide the two values to get

2/9 = 0.22

this is approximate

The final answer is 0.22

Answer 2

Probability of an event is the measurement of its chance of occurrence. The probability of P(AA or BB) for this case is given by: Option B: 0.22 approx

How to calculate the probability of an event?

Suppose that there are finite elementary events in the sample space of the considered experiment, and all are equally likely.

Then, suppose we want to find the probability of an event E.

Then, its probability is given as

$P(E) = \dfrac{\text{Number of favorable cases}}{\text{Number of total cases}} = \dfrac{n(E)}{n(S)}$

where favorable cases are those elementary events who belong to E, and total cases are the size of the sample space.

The possible outcomes for the considered experiment are:

AA BA CA

AB BB CB

AC BC CC

Thus, sample size is of 9 length (9 possible outcomes). Or, n(S) = 9

Now, let we define an event such that:

E = Occurrence of outcome as AA or BB

Then, the number of ways E can occur is: n(E) = 2

(since only one of AA or BB can occur at a time, and that they together  create only two ways for occurrence of E).

Thus, we get:

$P(E) = P(\text{AA or BB}) = \dfrac{n(E)}{n(S)} = \dfrac{2}{9} \approx 0.22$

Thus, the probability of P(AA or BB) for this case is given by: Option B: 0.22 approx

Learn more about probability here:

brainly.com/question/1210781