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NDA 2021
Exam
NDA
Year
2021
Subject
Mathematics
Chapter
Probability

NDA 2021 · Mathematics · Probability

If A and B are two events such that P(A)=(3)/(4) and P(B)=(5)/(8) ,...

If AA and BB are two events such that P(A)=34P(A)=\frac{3}{4} and P(B)=58P(B)=\frac{5}{8}, then consider the following statements : 1. The minimum value of P(A∪B)P(A \cup B) is 34\frac{3}{4}. 2. The maximum value of P(A∩B)P(A \cap B) is 58\frac{5}{8}. Which of the above statements is/are correct?

Options

  1. A11 only
  2. B22 only
  3. CBoth 11 and 22
  4. DNeither 11 nor 22

Correct answer

C. Both 11 and 22

Step-by-step solution

P(A)=34 and P(B)=58P(A∪B)=P(A)+P(B)−P(A∩B)\begin{aligned} & P(A)=\frac{3}{4} \text{ and } P(B)=\frac{5}{8} \\ & P(A \cup B)=P(A)+P(B)-P(A \cap B)\end{aligned}P(A \cup B)isis\minwhenwhenP(A \cap B)isis\maxi.e.i.e.\frac{5}{8}P(A \cup B)_{\min }=\frac{3}{4}+\frac{5}{8}-\frac{5}{8}=\frac{3}{4}$ Hence, both (1) and (2) are correct.
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