The dice are rolled until three points are rolled. Determine the likelihood that the dice will be rolled more than twice.

1. The probability of the event Ai that three points will be dropped on the i-th throw of the dice:

P (Ai) = 1/6.
2. Accordingly, the probability of the opposite event Ai ‘- not getting three points:

P (Ai ‘) = 1 – P (Ai);
P (Ai ‘) = 1 – 1/6 = 5/6.
3. The probability of the event B1 that three points will be rolled on the first roll of the dice:

P (B1) = P (A1) = 1/6.
4. Probability of B2 event that the first time three points are rolled on the second throw:

P (B2) = P (A1 ‘) * P (A2 | A1’);
P (B2) = 5/6 * 1/6 = 5/36.
5. The probability of the event S2 that three points will be rolled on the first two throws:

P (S2) = P (B1) + P (B2);
P (S2) = 1/6 + 5/36 = 11/36.
6. The likelihood of the opposite event S2 ‘that the first two throws do not drop three points:

P (S2 ‘) = 1 – P (S2);
P (S2 ‘) = 1 – 11/36 = 25/36 ≈ 0.6944.
Answer: 0.7.