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A signal which can be green …

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A signal which can be green or red with probability 4/5 and 1/5 respectivEly, is received by station A and then transmitted to station B. The probability of each receiving the signal correctly is 3/4. If the signal received at station B is green, then find the probability that original signal is green.

Posted by Shivang Puri 7 years, 1 month ago

CBSE > Class 12 > Mathematics

1 answers

Gurvinder Kaur 6 years, 2 months ago

Event G=original signal is green
{tex}{E_1}{/tex}=A receives the signal correct
{tex}{E_2}{/tex}=B receives the signal correct
E=signal received by B is green
P(signal received by B is green)={tex}P\left( {G{E_1}{E_2}} \right) + P\left( {G{{\overline E }_1}{{\overline E }_2}} \right) + P\left( {\overline G {E_1}{{\overline E }_2}} \right){/tex}
{tex}P\left( E \right) = \frac{{46}}{{5 \times 16}}{/tex}
{tex}P\left( {G/E} \right) = \frac{{40/5 \times 16}}{{46/5 \times 16}} = \frac{{20}}{{23}}{/tex}

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