asigurato7
2022-07-20
Answered

How do you use the Counting Principle to find the probability of rolling a 4 on each of 4 number cubes?

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Killaninl2

Answered 2022-07-21
Author has **20** answers

According to the Counting Principle, if there are two or more independent events, you find the probability of both/all of them happening as the product of their individual probabilities. In this case we have 4 independent rolls of the die and so we'll multiply the 4 probabilities together.

The probability of each roll to get a 4 on a 6-sided cube is 1/6. This means that the probability of rolling a 4 on each of four number cubes is:

$\left(\frac{1}{6}\right)\left(\frac{1}{6}\right)\left(\frac{1}{6}\right)\left(\frac{1}{6}\right)=\frac{1}{{6}^{4}}=\frac{1}{1296}$

The probability of each roll to get a 4 on a 6-sided cube is 1/6. This means that the probability of rolling a 4 on each of four number cubes is:

$\left(\frac{1}{6}\right)\left(\frac{1}{6}\right)\left(\frac{1}{6}\right)\left(\frac{1}{6}\right)=\frac{1}{{6}^{4}}=\frac{1}{1296}$

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