(a) Suppose that you throw 4 dice. Find the probability that...

(a) Suppose that you throw 4 dice. Find the probability that you get at least one 1 . (b) Suppose that you throw 2 dice 24 times. Find the probability that you get at least one $(1,1),$ that is, you roll "snake;-eyes." [Note: The probability of part (a) is greater than the probability of part (b).]

(a) Suppose that you throw 4 dice. Find the probability that you get at least one 1 .
(b) Suppose that you throw 2 dice 24 times. Find the probability that you get at least one $(1,1),$ that is, you roll "snake;-eyes." [Note: The probability of part (a) is greater than the probability of part (b).]

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Key Concepts

Complement Rule

The complement rule is a fundamental probability principle that states the probability of an event occurring is equal to one minus the probability of the event not occurring. This method is particularly useful for calculating the chance of 'at least one' occurrence by subtracting the probability of the event never occurring from one.

Independent Events

Independent events are those whose outcomes do not influence one another. In probability calculations for processes like multiple dice rolls, the overall probability of several independent events all occurring is found by multiplying their individual probabilities.

Repeated Trials in Probability

Repeated trials involve performing the same random experiment multiple times, where each trial is independent of the others. When calculating the probability of an event happening at least once over numerous, independent attempts, one typically uses the complement rule by first finding the probability of the event not occurring in any trial and then subtracting that from one.

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