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NDA 2019
Exam
NDA
Year
2019
Subject
Mathematics
Chapter
Probability

NDA 2019 · Mathematics · Probability

A and B are two events such that A and B are mutually exclusive. If...

A and B are two events such that A⃗\vec{A} and Bˉ\bar{B} are mutually exclusive. If P(A)=0.5P(A)=0.5 and P(B)=0.6P(B)=0.6, then what is the value of P(A∣B)P(A \mid B) ?

Options

  1. A15\frac{1}{5}
  2. B16\frac{1}{6}
  3. C25\frac{2}{5}
  4. D13\frac{1}{3}

Correct answer

B. 16\frac{1}{6}

Step-by-step solution

Aˉ\bar{A} and Bˉ\bar{B} are mutually exclusive ∴P(Aˉ∩Bˉ)=0\therefore P(\bar{A} \cap \bar{B})=0 Given, P(A)=0.5⇒P(Aˉ)=1−0.5=0.5\mathrm{P}(\mathrm{A})=0.5 \Rightarrow P(\bar{A})=1-0.5=0.5P(B)=0.6⇒P(Bˉ)=1−0.6=0.4P(A∣B)=P(A∩B)P(B)=1−P(Aˉ∪Bˉ)P(B)=1−(P(Aˉ)+P(Bˉ))P(B)=1−(0.5+0.4)0.6=1−0.90.6=0.10.6=16\begin{aligned} & \mathrm{P}(\mathrm{B})=0.6 \Rightarrow P(\bar{B})=1-0.6=0.4 \\ & P(A \mid B)=\frac{P(A \cap B)}{P(B)}=\frac{1-P(\bar{A} \cup \bar{B})}{P(B)} \\ & =\frac{1-(P(\bar{A})+P(\bar{B}))}{P(B)}=\frac{1-(0.5+0.4)}{0.6} \\ & =\frac{1-0.9}{0.6}=\frac{0.1}{0.6}=\frac{1}{6}\end{aligned}$$
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