Question

If a and b are two events such that p(a) = 0.2, p(b) = 0.6 and p(a /b) = 0.2 then the value of p(a /~b) is

Answer 1

$\textbf{Given:}$

$\mathsf{P(A)=0.2,\;P(B)=0.6,\;P\left(\dfrac{A}{B}\right)=0.2}$

$\textbf{To find:}$

$\textsf{The value of}$

$\mathsf{P\left(\dfrac{A}{\overline{B}}\right)}$

$\textbf{Solution:}$

$\mathsf{Consider,}$

$\mathsf{P\left(\dfrac{A}{B}\right)=0.2}$

$\mathsf{\dfrac{P(A{\cap}B)}{P(B)}=0.2}$

$\mathsf{\dfrac{P(A{\cap}B)}{0.6}=0.2}$

$\implies\mathsf{P(A{\cap}B)=0.12}$

$\mathsf{Now,}$

$\mathsf{P\left(\dfrac{A}{\overline{B}}\right)}$

$\mathsf{=\dfrac{P(A{\cap}\overline{B})}{P(\overline{B})}\right}$

$\mathsf{=\dfrac{P(A)-P(A{\cap}B)}{1-P(B)}}$

$\mathsf{=\dfrac{0.2-0.12}{1-0.6}}$

$\mathsf{=\dfrac{0.08}{0.4}}$

$\mathsf{=\dfrac{8}{40}}$

$\mathsf{=\dfrac{1}{5}}$

$\implies\boxed{\mathsf{P\left(\dfrac{A}{\overline{B}}\right)=\dfrac{1}{5}}}$

$\textbf{Find more:}$

If a and b are two sets so that n(b-a)=2n(a-b) =4n(aΠb) and if n(aub)=14,then find n(p(a))​

https://brainly.in/question/22363737

A and b are events such that p(a u b)=3/4 p(a n b)=1/4 p(a bar)=2/3 then p(abar n b)is

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Answer 2

$\textbf{Given:}$

$\mathsf{P(A)=0.2,\;P(B)=0.6,\;P\left(\dfrac{A}{B}\right)=0.2}$

$\textbf{To find:}$

$\textsf{The value of}$

$\mathsf{P\left(\dfrac{A}{\overline{B}}\right)}$

$\textbf{Solution:}$

$\mathsf{Consider,}$

$\mathsf{P\left(\dfrac{A}{B}\right)=0.2}$

$\mathsf{\dfrac{P(A{\cap}B)}{P(B)}=0.2}$

$\mathsf{\dfrac{P(A{\cap}B)}{0.6}=0.2}$

$\implies\mathsf{P(A{\cap}B)=0.12}$

$\mathsf{Now,}$

$\mathsf{P\left(\dfrac{A}{\overline{B}}\right)}$

$\mathsf{=\dfrac{P(A)-P(A{\cap}B)}{1-P(B)}}$

$\mathsf{=\dfrac{0.2-0.12}{1-0.6}}$

$\mathsf{=\dfrac{0.08}{0.4}}$

$\mathsf{=\dfrac{8}{40}}$

$\mathsf{=\dfrac{1}{5}}$

$\implies\boxed{\mathsf{P\left(\dfrac{A}{\overline{B}}\right)=\dfrac{1}{5}}}$