Two dice are thrown. What is the probability that: a) the total of the dropped out points is 12,

Two dice are thrown. What is the probability that: a) the total of the dropped out points is 12, b) the total of the dropped out points is 11, c) the total of the dropped out points is not less than 9, d) at least one of the dice is 1?

a) The sum of the points dropped on two dice is 12 if each dice has a six. The probability of a six on one die is 1/6, the probability of a six on both bones is 1/6 * 1/6 = 1/36

b) The sum of points on two dice equal to 11 can be achieved in two ways: on the first dice there are six to the second five, or vice versa. The probability of each of the events is 1/36. The probability of sum 11 on two dice is 1/36 + 1/36 = 1/18.

c) The sum of points not less than 9 is achieved in ten ways: 3 and 6; 4 and 5; 4 and 6; 5 and 4; 5 and 5; 5 and 6; 6 and 3; 6 and 4; 6 and 5; 6 and 6. Probability 10 * 1/36 = 5/18.

d) The probability of not dropping one on one bone is 5/6, on two bones 5/6 * 5/6 = 25/36.

The probability that at least one die will roll 1 is 1 – 25/36 = 11/36.

Answer:

a) 1/36; b) 1/18; c) 5/18; d) 11/36