Question

Laila is interested to buy dish detergent. The probability to buy detergent brand A is 45%, the probability to buy detergent brand B is 35%. The probability to buy both brands is 30% What is the probability Laila to buy brand A or Brand B or both?
A) 0.45 + 0.35
B) 0.45 + 0.35 - 0.30
C) 0.45 - 0.35 - 0.30
D) 0.45 + 0.35 + 0.30
E) (0.45) (0.35) - 0.30

Answer 1

To find the probability that Laila buys either brand A or brand B or both, we can use the principle of inclusion-exclusion. The formula for the probability of either event A or event B (or both) is:

\[ P(A \cup B) = P(A) + P(B) - P(A \cap B) \]

Where:
- \( P(A) \) is the probability of buying brand A (0.45),
- \( P(B) \) is the probability of buying brand B (0.35),
- \( P(A \cap B) \) is the probability of buying both brands (0.30).

Plugging in the given values:

\[
P(A \cup B) = 0.45 + 0.35 - 0.30
\]

Calculating this gives:

\[
P(A \cup B) = 0.80 - 0.30 = 0.50
\]

Now, we can determine which option corresponds to our solution:

**Correct answer:** **B) \( 0.45 + 0.35 - 0.30 \)**