Three robots are tested for synchronization in remote communication and are kept in different places. The first one would beep or light with probabilities 2/3 and 1/3 respectively. The second one would receive and communicate the same to the third. The second and third robots would transmit with a precision of 80%. Let p be the probability that the third robot beeps, when the first one actually lighted. Then 31 p equals:

Question

Three robots are tested for synchronization in remote communication and are kept in different places. The first one would beep or light with probabilities \( \frac{2}{3} \) and \( \frac{1}{3} \) respectively. The second one would receive and communicate the same to the third. The second and third robots would transmit with a precision of \( 80 \% \). Let p be the probability that the third robot beeps, when the first one actually lighted. Then 31 p equals