two number cubes each with faces numbered 1 through 6, are tossed. What is the probability that 2 will come up on each cube?
If the events are independent, the probability of both/all events occurring is determined by multiplying the probabilities of the individual events.
1/6 * 1/6 = ?
To find the probability that two will come up on each cube when two number cubes are tossed, we need to determine the number of favorable outcomes and the total number of possible outcomes.
Step 1: Determine the number of favorable outcomes.
To have two come up on each cube, we need both number cubes to show the number two on their faces. Since each cube has six faces with numbers 1 through 6, the probability of getting a two on one cube is 1/6. Therefore, the probability of getting two on both cubes is (1/6) * (1/6) = 1/36.
Step 2: Determine the total number of possible outcomes.
When two number cubes are tossed, the total number of possible outcomes is the product of the number of faces on each cube. Since each cube has six faces, the total number of possible outcomes is 6 * 6 = 36.
Step 3: Calculate the probability.
The probability is determined by dividing the number of favorable outcomes by the total number of possible outcomes. In this case, it is 1/36 divided by 36, which simplifies to 1/36.
Therefore, the probability that two will come up on each cube when two number cubes are tossed is 1/36.