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40% of cereal boxes contain a prize. What is the probability of getting a prize if I buy 3 or less boxes of cereal?

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Answer:

0.784 or 78.4%.

Explanation:

To calculate the probability of getting a prize if you buy 3 or fewer boxes of cereal, we need to consider the complementary probability. The complementary probability is the probability of the event not happening.

Let's calculate the probability of not getting a prize in a single box of cereal:

Probability of not getting a prize = 1 - Probability of getting a prize

Probability of not getting a prize = 1 - 0.40

Probability of not getting a prize = 0.60

Since the events are independent (each box has the same probability), we can multiply the probabilities. To find the probability of not getting a prize in multiple boxes, we multiply the individual probabilities together.

Let's calculate the probability of not getting a prize in three boxes of cereal:

Probability of not getting a prize in 3 boxes = (Probability of not getting a prize)^3

Probability of not getting a prize in 3 boxes = 0.60^3

Probability of not getting a prize in 3 boxes ≈ 0.216

Now, to find the probability of getting a prize, we subtract the probability of not getting a prize from 1:

Probability of getting a prize in 3 or fewer boxes = 1 - Probability of not getting a prize in 3 boxes

Probability of getting a prize in 3 or fewer boxes = 1 - 0.216

Probability of getting a prize in 3 or fewer boxes ≈ 0.784

Therefore, the probability of getting a prize if you buy 3 or fewer boxes of cereal is approximately 0.784 or 78.4%.

User Skarface
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