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A pair of 6 sided dice are tossed. What is the probability that at least one of the dice has a value greater than or equal to 3?

User Ludwiguer
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Final answer:

To find the probability that at least one of the dice has a value greater than or equal to 3, we need to calculate the probability of the complementary event, which is the event that neither of the dice has a value greater than or equal to 3. The probability is 8/9.

Step-by-step explanation:

To find the probability that at least one of the dice has a value greater than or equal to 3, we need to calculate the probability of the complementary event, which is the event that neither of the dice has a value greater than or equal to 3. Let's first find the probability of getting a value less than 3 on one die. There are two values less than 3, which are 1 and 2, out of a total of six possible outcomes:

P(One die has a value less than 3) = 2/6 = 1/3

Since rolling a pair of dice are independent events, we can multiply the probabilities to find the probability of both dice having values less than 3:

P(Both dice have values less than 3) = (1/3) * (1/3) = 1/9

Finally, we can subtract this probability from 1 to find the probability of at least one die having a value greater than or equal to 3:

P(At least one die has a value greater than or equal to 3) = 1 - P(Both dice have values less than 3) = 1 - 1/9 = 8/9

User Sundar Nataraj
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