Signal Probability

Probability Level 3

A signal which can be green or red with probability $\frac{4}{5}$ and $\frac{1}{5}$ respectively, is received by station A and then transmitted to station B. The probability of each station receiving the signal correctly is $\frac{3}{4}$ . If the signal received at station B is green, then the probability that the original signal was green is:

\frac{6}{7}

\frac{20}{23}

\frac{3}{5}

\frac{9}{20}

1 solution

Sid Patak
Jun 3, 2020

Let A = color at station A.

Let B = color at station B.

Let O = color at original station.

We need to compute: P(O=green | B=green ).

This is equal to P(O=green &&B=green) / P(B=green).

Using the figure this is 20/23 .

Signal Probability

1 solution

0 pending reports