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%.