A construction company has recently built a hotel. The probability that the new hotel will get an award for its design is 0.28, and the probability that it will get an award for the efficient use of materials is 0.13. If the probability that it will get at least one award is 0.36, what is the probability that it will get both awards?

#### Solution

Let $A$ be the event that the new hotel will get an award for its design.

Let $B$ be the event that the new hotel will get an award for the efficient use of materials.

Given that $P(A) = 0.28$, $P(B) = 0.13$.

The probability that it will get at least one award is 0.36, i.e., $P(A\cup B)= 0.36$.

The probability that it will get both awards is $P(A\cap B)$.

Thus,

` $$ \begin{aligned} P(A\cap B) &= P(A) + P(B) - P(A\cup B)\\ &= 0.28 + 0.13 - 0.36\\ &= 0.05 \end{aligned} $$ `

#### Further Reading

- Statistics
- Descriptive Statistics
- Probability Theory
- Probability Distribution
- Hypothesis Testing
- Confidence interval
- Sample size determination
- Non-parametric Tests
- Correlation Regression
- Statistics Calculators