Question

Five dice (6 sided) are rolled. Find the probability that 5 ones are obtained (ie 5 dice showing a one). Explain fully and show each step.

Answer 1

The probability of rolling five ones with five six-sided dice is calculated by multiplying the probability of obtaining a one on a single die, which is 1/6, by itself five times, leading to a final answer of 1/7776.

Step-by-step explanation:

The question asks for the probability of rolling five ones with five six-sided dice. Each die roll is independent, and the probability of getting a one on a single die is 1/6 because there are six possible outcomes and only one favorable outcome which is getting a one. To find the probability of getting five ones with all five dice, we multiply the probability of getting a one on a single die by itself five times since each die is independent of the others.

The probability for one die is 1/6, and so for five dice:

1. Calculate the probability for one die: P(one) = 1/6
2. Since the dice are independent, raise the single-die probability to the power of 5: P(five ones) = (1/6)^5
3. Compute the probability: P(five ones) = (1/6)^5 = 1/7776

The probability of rolling five ones with five dice is 1/7776.