If $P(A) = 0.4$ and $P(B) = 0.5$ and $P(A \cap B) = 0.2$, then $P(A \cup B)$ is
A$0.9$
B$0.7$
C$0.2$
D$1.1$
Answer & Solution
Correct answer: B. $0.7$
1. Apply the addition rule: $P(A \cup B) = P(A) + P(B) - P(A \cap B)$.
2. Substitute: $P(A \cup B) = 0.4 + 0.5 - 0.2 = 0.7$.
3. Sanity check: $P(A \cup B)$ must be $\leq 1$ (it's a probability) AND $\geq$ each individual $P(A), P(B)$. Both satisfied: $0.7 \geq 0.5 \geq 0.4$. ✓
4. Option A forgets to subtract $P(A \cap B)$ (gives $0.9$, also valid). Option C is just $P(A \cap B)$ confusing union with intersection. Option D ($1.1$) is impossible — probabilities never exceed 1.
_Source: NCERT Class 11 Mathematics, Ch 14, §14.2.3 (Addition rule, numerical examples), p. 11._
Related questions
Simplifying an equation, a student reaches a statement that can never be true. The equatioAfter squaring both sides of a radical equation, a student finds a root that fails the oriSolving such an equation, a student clears every denominator at once by multiplying througAn equation contains at least one rational expression, with a variable in a denominator. TTo clear a complex number from a denominator, a student multiplies by the term found by flComplex numbers cannot sit on an ordinary number line, so they are plotted on a plane whosRather than drawing a number line, a student writes the solution set with brackets and parA statement joins two inequalities together in one line, such as 2 < x < 7. That statement