Question

The probability that a new airport will get an award for its design is 0.16, the
probability that it will get an award for the efficient use of materials is 0.24 and the
probability that it will get both the awards is 0.11.
(a) what is the probability that it will get atleast one of the two awards?
(b) what is the probability that it will get only one of the two awards?

Answer 1

Answer on Question #45600 – Math – Statistics and Probability

Question

The probability that a new airport will get an award for its design is 0.16, the probability that it will get an award for the efficient use of materials is 0.24 and the probability that it will get both the awards is 0.11.

(a) what is the probability that it will get at least one of the two awards?

(b) what is the probability that it will get only one of the two awards?

Solution

Let event $A =$ "airport will get an award for its design",

$B =$ "airport will get an award for the efficient use of materials".

Then $P(A) = 0.16, P(B) = 0.24, P(A \cap B) = 0.11$.

(a) $P(A \cup B) = P(A) + P(B) - P(A \cap B) = 0.16 + 0.24 - 0.11 = 0.29$;

(b) $P(A \setminus B) + P(B \setminus A) = P(A) - P(A \cap B) + P(B) - P(A \cap B) =$

$$= P(A) + P(B) - 2P(A \cap B) = 0.16 + 0.24 - 2 \cdot 0.11 = 0.18.$$

Answer.

(a) 0.29

(b) 0.18

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