0 like 0 dislike
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?

0 like 0 dislike
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)
by
0 like 0 dislike
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?
by
0 like 0 dislike
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)
by
0 like 0 dislike
Also P(B|A), which is in the formula you list, is the same as P(AB)P(A).
by
0 like 0 dislike
P(A|B) = P(AB)/P(B). So P(AB) = P(A|B)P(B). There is your P(AB), ok?
by
0 like 0 dislike
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)?
by
0 like 0 dislike
george357 said: But Bayes'theorem doesn't have P(AB)! Click to expand... Show your work, especially where you need to know p(AB).
by
0 like 0 dislike
CaptainBlack said: Again; Bayes'theorem. Click to expand... But Bayes'theorem doesn't have P(AB)!
by
0 like 0 dislike
Again; Bayes'theorem.
by