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If you roll two fair six-sided dice, what is the probability that at least one
die shows a 3?

Answer 1

The probability that at least one die shows a 3 when two six-sided dice are rolled is 11/36, calculated using the complement rule.

Step-by-step explanation:

The question asks for the probability that at least one die shows a 3 when two fair six-sided dice are rolled.

To solve this, we can use the concept of complementary probability, which means finding the probability that the event does not occur and subtracting it from 1.

The probability that a single die does not show a 3 is 5/6 since there are five other outcomes.

When rolling two dice, we multiply the individual probabilities for independent events, so the probability that neither die shows a 3 is (5/6) x (5/6).

Subtracting this from 1 gives us the probability that at least one die shows a 3:

1 - (5/6) x (5/6) = 1 - (25/36)

= 11/36

Therefore, the probability that at least one die shows a 3 is 11/36.