A fair number cube has faces numbered from 1 to 6. When the number cube is rolled, the theoretical probability of it landing on a multiple of 3 is one over three.. What is the theoretical probability of the number cube NOT landing on a multiple of 3?

Explanation:

The theoretical probability of landing on a multiple of three is 1/3

So the theoretical probability of not landing on a multiple of three is 1-(1/3) = 3/3-1/3 = (3-1)/3 = 2/3

We can think of 1/3 to mean "1 out of 3 times", while 2/3 means "2 out of 3 times".

2/3

Step-by-step explanation:

We can find this in two ways:

1. Finding the numbers that aren't multiples of three

2. Subtracting 1/3 from 3/3

Let's do both ways:

1. These numbers are multiples of 3: 3 and 6

This leaves these numbers: 1, 2, 4, 5

Since there is 4 numbers there we can divide 4/6, or that simplifies down to 2/3. So, the theoretical probability that the number cube does not land on a multiple of 3 is 2/3.

2. Now this is the easier way to do it. Since we know that the probabilities have to add up to 1, we can just subtract 1/3 from 3/3 (because 3/3 equals one and subtracting fractions needs the same denominator)

3/3 - 1/3 = 2/3

This once again shows that the probability of not rolling a multiple of 3 is 2/3.

Hope this helps!!

- Kay :)

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