Final answer:
The probability of the airport getting at least one reward is 0.44, the probability of getting only one reward is 0.31, the probability of getting at most one reward is 0.87, the probability of getting less than two rewards is 0.57, the probability of getting less than one reward is 0.18, the probability of getting more than one reward is 0.43, and the probability of getting less than three rewards is 0.7.
Step-by-step explanation:
To find the probability that the airport will get at least one reward, we can use the formula P(A or B) = P(A) + P(B) - P(A and B), where A represents the award for design and B represents the award for efficient use of materials. Substituting the values given, we have P(A or B) = 0.18 + 0.39 - 0.13 = 0.44.
To find the probability that the airport will get only one reward, we need to find P(A or B) - P(A and B), which gives us 0.44 - 0.13 = 0.31.
To find the probability that the airport will get at most one reward, we can subtract the probability of getting both rewards from 1, which gives us 1 - 0.13 = 0.87.
To find the probability that the airport will get less than two rewards, we can use the formula P(x < 2) = P(x = 0) + P(x = 1), which gives us 0.18 + 0.39 = 0.57.
To find the probability that the airport will get less than one reward, we can use the formula P(x < 1) = P(x = 0), which gives us 0.18.
To find the probability that the airport will get more than one reward, we can use the formula P(x > 1) = 1 - P(x < 2), which gives us 1 - 0.57 = 0.43.
To find the probability that the airport will get less than three rewards, we can use the formula P(x < 3) = P(x = 0) + P(x = 1) + P(x = 2), which gives us 0.18 + 0.39 + 0.13 = 0.7.