Question

A dice is thrown twice. the sum of a's scores is odd, b's score is the same. find the probability that a combines with b.

Answer 1

To find the probability that A combines with B, we first determine the probabilities of each event and then multiply them together.

Step-by-step explanation:

To find the probability that A combines with B, we need to first determine the number of favorable outcomes for A and B, as well as the total number of possible outcomes. Let's break it down:

Event A: both dice show an even number. There are 6 even numbers on a 12-sided die, so P(A) = 6/12 = 1/2.

Event B: both dice show a number greater than eight. There are 3 numbers greater than eight on a 12-sided die, so P(B) = 3/12 = 1/4.

To find the probability that A combines with B (P(A and B)), we multiply the probabilities of A and B, since both events need to occur together: P(A and B) = P(A) * P(B) = (1/2) * (1/4) = 1/8.