Question

When using a 6 sided cube, what is the probability of rolling a 3, then not rolling a 3, and then rolling an even number?

Answer 1

5/72

Explanation:

You want the probability of rolling a 6-sided die 3 times with the sequential outcomes 3, not 3, even number.

Sequential outcomes

The probability of any given sequence of outcomes is the product of the probabilities of the outcomes individually. (We assume independence.)

P(3) = 1/6

P(not 3) = 1 -P(3) = 5/6

P(even) = 1/2

Then the probability of the given sequence is ...

P(3, 3', even) = (1/6)(5/6)(1/2) = 5/72

The probability of the given sequence is 5/72.

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Additional comment

The outcomes are independent if the probability of occurrence does not depend on any previous outcome.