Respuesta :
Answer:
a) 0.6667 = 66.67% probability that a 0 is received.
b) 0.9 = 90% probability that a 0 was transmitted, given that a 0 was received.
Step-by-step explanation:
Bayes Theorem:
Two events, A and B.
[tex]P(B|A) = \frac{P(B)*P(A|B)}{P(A)}[/tex]
In which P(B|A) is the probability of B happening when A has happened and P(A|B) is the probability of A happening when B has happened.
(a) Find the probability that a 0 is received.
0.9 of 2/3(0 received when a 0 is sent).
0.2 of 1/3(0 received when a 1 is sent). So
[tex]p = \frac{0.9*2}{3} + \frac{0.2*1}{3} = 0.6667[/tex]
0.6667 = 66.67% probability that a 0 is received.
(b) Use Bayes theorem to find the probability that a 0 was transmitted, given that a 0 was received.
Event A: 0 received
Event B: 0 transmitted.
0.6667 = 66.67% probability that a 0 is received, which means that [tex]P(A) = 0.6667[/tex]
A zero is transmitted two-thirds of time, which means that [tex]P(B) = 0.6667[/tex]
When a 0 is sent, the probability that it is received correctly is 0.9, which means that [tex]P(B|A) = 0.9[/tex]
So
[tex]P(B|A) = \frac{P(B)*P(A|B)}{P(A)} = \frac{0.6667*0.9}{0.6667} = 0.9[/tex]
0.9 = 90% probability that a 0 was transmitted, given that a 0 was received.
