First slide

Theorems of probability

Question

$A signal which can be green or red with probability (\frac{4}{5}) and (\frac{1}{5}) respectively is received$ $by the station A and Transmitted to B . The probability of each station receiving signal$ $correctly is \frac{3}{4} . If signal in received in B is green. The probability original signal was$ green is

Difficult

A

$\frac{3}{5}$
B

$\frac{6}{7}$
C

$\frac{20}{23}$
D

$\frac{9}{20}$

Solution

$G = Original signal green. A = A receive correct signal, B = B receive signal correct. E$ $is signal received by B is green.$
$P (\frac{G}{E}) = \frac{P (G \cap E)}{P (E)}$
$P (E) = P (G A B) + P (G \bar{A} \bar{B}) + P (\bar{G} A \bar{B}) + P (\bar{G} \bar{A} B)$
$= \frac{4}{5} . \frac{3}{4} . \frac{3}{4} + \frac{4}{5} . \frac{1}{4} . \frac{1}{4} + \frac{1}{5} . \frac{3}{4} . \frac{1}{4} + \frac{1}{5} . \frac{1}{4} . \frac{3}{4} = \frac{46}{80}$
$P (G \cap E) = P (G A B) + P (G \bar{A} \bar{B}) = \frac{40}{80}$
$∴ P (\frac{G}{E}) = \frac{P (G \cap E)}{P (E)} = \frac{20}{23}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App