Answer:
b. (1/6)⁵
Explanation:
To calculate the probability of Roku rolling all 1s when he rolls 5 fair, 6-sided dice at once, we need to determine the probability of rolling a 1 on each individual die and then multiply those probabilities together.
Each die has 6 possible outcomes (numbers 1 to 6), and we want to roll a 1 on each of the 5 dice. The probability of rolling a 1 on a single die is 1 out of 6, or 1/6.
Since we are rolling 5 dice simultaneously, we need to multiply the probabilities together. Therefore, the probability of rolling all 1s is (1/6) * (1/6) * (1/6) * (1/6) * (1/6), which simplifies to (1/6)^5.
So, the correct answer is option b. (1/6)^5.
Further Explanation: Now, let's understand why this is the correct answer. When we roll the first die, there is a 1/6 chance of getting a 1. Similarly, when we roll the second die, there is also a 1/6 chance of getting a 1. Since the dice are fair and independent, the probability of getting a 1 on each die is the same, 1/6. Therefore, we multiply the probabilities together to find the probability of rolling all 1s on all 5 dice.
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