Case 1: If the initial roll is less than 4, you roll two dice and sum the results.

In this case, the possible outcomes that result in a sum of 6 are:

1 + 5 = 6

2 + 4 = 6

3 + 3 = 6

4 + 2 = 6

5 + 1 = 6

The total number of outcomes in this case is 5 * 6 = 30 (since each dice has 6 sides). However, we only consider the outcomes where the sum is 6, so the probability in this case is 5/30 = 1/6.

Case 2: If the initial roll is greater than 4, you roll only one dice and use the result.

In this case, the possible outcome that results in a final result of 6 is rolling a 6 on the dice.

The total number of outcomes in this case is 6 (since each dice has 6 sides), and only one of those outcomes results in a final result of 6. Therefore, the probability in this case is 1/6.

Now, we need to calculate the probability of each case occurring.

The probability of the initial roll being less than 4 is 3/6 (since there are three possible outcomes: 1, 2, and 3).

The probability of the initial roll being greater than 4 is 3/6 (since there are three possible outcomes: 5, 6).

Finally, we calculate the overall probability by considering both cases:

P(final result of 6) = P(less than 4) * P(sum of 6 | less than 4) + P(greater than 4) * P(result of 6 | greater than 4)

= (3/6) * (1/6) + (3/6) * (1/6)

= 3/36 + 3/36

= 6/36

= 1/6

Therefore, the probability of getting a final result of 6 after this experiment is 1/6 or approximately 0.1667.

Why result <> 1/6? Can anyone explain for me