Question

A circuit contains two switches. The first switch transmits messages correctly 80 percent of the time, and the second switch transmits messages correctly 90 percent of the time. What percent of the time will the message be transmitted successfully through both switches?

Answer 1

Answer:

72%

Step-by-step explanation:

A circuit contains two switches.

The first switch transmits messages correctly 80% of the time, then the probability that the message will be transmitted successfully through the first switch is

$p_1=0.8$

The second switch transmits messages correctly 90% of the time, then the probability that the message will be transmitted successfully through the second switch is

$p_2=0.9$

The probability that the message will be transmitted successfully through both switches is

$p=p_1\cdot p_2=0.8\cdot 0.9=0.72$

that is exactly 72%