Answer:
The probability is 25/216. Approximately 0.116
Step-by-step explanation:
You need
- The first throw to fail (probability 1-1/6 = 5/6)
- The second throw to fail (probability 5/5)
- The third throw to be a success (probability 1/6)
Since each throw is independent of the others, we have to multiply all probabilities to obtain the total probability of the event. Thus, the probability of requiring 3 rolls until getting doubles is
5/6 * 5/6 * 1/6 = 25/216 = 0.115741
This problem can also be solved with sophisticated theory;
the random variable which counts the number of tries until the first success is a geometric distribution. The only parameter of the distribution is the probability of success p. If X is geometric with parameter p, then the probability of X being equal to k (in other words, requiring k tries for a success) is
P(X = k) = (1-p)^(k-1) * p
If p = 1/6, then
P(X = 2) = (1-1/6)^2*(1/6) = (5/6)²*1/6 = 25/216