In a certain game, a player throws a standard 6-sided number cube twice per turn. What is the probability that the result of the first throw will be a 1, and the result of the second throw will be greater than 3?
To find the probability that the first throw results in a 1 and the second throw results in a number greater than 3, we need to calculate the probabilities of both events separately and then multiply them together.
First, let's find the probability of getting a 1 on the first throw. Since the number cube is standard, it has 6 equally likely outcomes (1, 2, 3, 4, 5, and 6). Out of these 6 outcomes, only 1 is desired (getting a 1). Therefore, the probability of getting a 1 on the first throw is 1/6.
Next, let's find the probability of getting a number greater than 3 on the second throw. Out of the 6 equally likely outcomes, there are 2 outcomes that are greater than 3 (4, 5, and 6). Therefore, the probability of getting a number greater than 3 on the second throw is 2/6, which simplifies to 1/3.
To find the probability of both events occurring, we multiply the probabilities together:
Probability = (Probability of first throw being 1) × (Probability of second throw being greater than 3)
= (1/6) × (1/3)
= 1/18
Therefore, the probability that the result of the first throw will be a 1 and the result of the second throw will be greater than 3 is 1/18.