Q253 / 270 · NDA 2025 (Phase 2) · Mathematics
The probability that a family owns a laptop is $0.68$; that it also owns a desktop is $0.56$. If the probability that it owns both is $0.48$, then what is the probability that a randomly selected family owns a laptop or a desktop?
- A$0.80$
- Correct answerB$0.76$
- C$0.36$
- D$0.28$
Solution
Let $L$ be the event that a family owns a laptop and $D$ be the event that a family owns a desktop.
Given:
$P(L) = 0.68$
$P(D) = 0.56$
$P(L \cap D) = 0.48$
The probability that a randomly selected family owns a laptop or a desktop is given by $P(L \cup D)$.
Using the addition theorem of probability:
$P(L \cup D) = P(L) + P(D) - P(L \cap D)$
Substituting the given values:
$P(L \cup D) = 0.68 + 0.56 - 0.48$
$P(L \cup D) = 1.24 - 0.48 = 0.76$
Given:
$P(L) = 0.68$
$P(D) = 0.56$
$P(L \cap D) = 0.48$
The probability that a randomly selected family owns a laptop or a desktop is given by $P(L \cup D)$.
Using the addition theorem of probability:
$P(L \cup D) = P(L) + P(D) - P(L \cap D)$
Substituting the given values:
$P(L \cup D) = 0.68 + 0.56 - 0.48$
$P(L \cup D) = 1.24 - 0.48 = 0.76$
Hence, the correct answer is option: 'B'.