One rule of probability can be expressed as the following: The probability of two independent events occurring simultaneously is the product of the probability of their occurring separately. If, for example, you had a pair of dice and rolled each die one at a time, what would be the probability that you would get two 4s? On the first roll, you would have a 1/6 chance. On the second roll, you would have a 1/6 chance. The probability of obtaining two 4s would be 1/6 x 1/6 = 1/36. Suppose you were playing a game with five dices. What is the chance of rolling a 6 on all five dice?
To calculate the probability of rolling a 6 on all five dice, we need to find the probability of rolling a 6 on a single die and multiply it by itself five times since we have five dice.
The probability of rolling a 6 on a single die is 1/6, as there are six possible outcomes (numbers 1 to 6) and only one favorable outcome (rolling a 6).
So, the probability of rolling a 6 on all five dice would be (1/6)^5 = 1/7776.
To calculate the probability of rolling a 6 on all five dice, you can again apply the rule of probability for independent events.
First, determine the probability of rolling a 6 on a single die. Since there are six equally likely outcomes (numbers 1 to 6) on each die roll, the probability of rolling a 6 on one die is 1/6.
Since each die roll is independent, the probability of rolling a 6 on all five dice is the product of the individual probabilities. So, the probability of rolling a 6 on all five dice would be (1/6) x (1/6) x (1/6) x (1/6) x (1/6), which simplifies to (1/6)^5 or 1/7776.
Therefore, the chance of rolling a 6 on all five dice is 1 in 7776 or approximately 0.0001286 (or 0.01286%)