Dot and Dash Signals

Question

In transmitting dot and dash signals, a communications system changes 0.25 of the dots to dashes and 1/3 of the dashes to dots. If 40% of the signals transmitted are dots and 60% are dashes, what is the probability that a dot received was actually a transmitted dot? I will let A to be the event a dot transmitted and B, the event a dot received, then we want to find P(AB)? This is just a starting strategy and I want to know if my thinking is correct to attack the problem?

Answer 1

Just for the record in your first equation you could have just said that P(A|B) = P(AB)/P(B). You did not have to even mention P(B|A)P(A)/P(B)

Answer 2

Jomo said: P(A|B) = P(AB)/P(B). So P(AB) = P(A|B)P(B). There is your P(AB), ok? Click to expand... Nice. CaptainBlack said: Bayes' theorem is the trivial conditional probability relation: P(A & B)=P(A|B)P(B)=P(B|A)P(A) Click to expand... Nice. A lot of formulas and ideas are filling my secret note. I will try to do it this time. \(\displaystyle P(A | B) = \frac{P(B | A)P(A)}{P(B)} = \frac{P(AB)}{P(B)}\) I hope that things will become easier now. \(\displaystyle P(AB) = P(A | B)P(B)\) Now we will find the probability of a dot received was a transmitted dot. I think that \(\displaystyle P(B) = 0.6\) The probability of dot received given dot transmitted was not given in the problem?! What should I do?

Answer 3

george357 said: Bayes' Theorem \(\displaystyle P(A | B) = \frac{P(B | A)P(A)}{P(B)} \) Where is P(AB)? Click to expand... Bayes' theorem is the trivial conditional probability relation: P(A & B)=P(A|B)P(B)=P(B|A)P(A)

Answer 4

Also P(B|A), which is in the formula you list, is the same as P(AB)P(A).

Answer 5

P(A|B) = P(AB)/P(B). So P(AB) = P(A|B)P(B). There is your P(AB), ok?

Answer 6

Jomo said: Show your work, especially where you need to know p(AB). Click to expand... Bayes' Theorem \(\displaystyle P(A | B) = \frac{P(B | A)P(A)}{P(B)} \) Where is P(AB)?

Answer 7

george357 said: But Bayes'theorem doesn't have P(AB)! Click to expand... Show your work, especially where you need to know p(AB).

Answer 8

CaptainBlack said: Again; Bayes'theorem. Click to expand... But Bayes'theorem doesn't have P(AB)!

Answer 9

Again; Bayes'theorem.