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NDA 2021
Exam
NDA
Year
2021
Subject
Mathematics
Chapter
Probability

NDA 2021 · Mathematics · Probability

If P(A B)=(5)/(6), P(A B)=(1)/(3) and P( A )=(1)/(2) , then which...

If P(A∪B)=56,P(A∩B)=13P(A \cup B)=\frac{5}{6}, P(A \cap B)=\frac{1}{3} and P(Aˉ)=12P(\bar{A})=\frac{1}{2}, then which of the following is/are correct? 1. AA and BB are independent events. 2. AA and BB are mutually exclusive events. Select the correct answer using the code given below.

Options

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

Correct answer

A. 11 only

Step-by-step solution

P(Aˉ)=12∴P(A)=1−P(Aˉ)=1−12=12\begin{aligned} & P(\bar{A})=\frac{1}{2} \\ & \therefore P(A)=1-P(\bar{A})=1-\frac{1}{2}=\frac{1}{2}\end{aligned} and P(B)=P(A∪B)−P(A)+P(A∩B)=56−12+13=23\begin{aligned} & \text{ and } P(B)=P(A \cup B)-P(A)+P(A \cap B) \\ & =\frac{5}{6}-\frac{1}{2}+\frac{1}{3}=\frac{2}{3}\end{aligned}Now,Now,P(A \cap B)=P(A) . P(B)=\frac{1}{2} \times \frac{2}{3}=\frac{1}{3}\therefore A$ and B are independent events.
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