Morse code uses "dots" and "dashes," which are known to occur in the proportion of 3:4. This means that for any given symbol, P(dot sent) = 3/7 and P(dash sent) = 4/7. Unfortunately, when coded messages are sent, there are sometimes errors in transmission. Suppose there is interference on the transmission line, and with probability 1/8 a dot is mistakenly received as a dash, and vice versa. a) What is the probability that the received symbol is a dot?

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JeanaShupp JeanaShupp · Answer 1 · 2020-10-25T03:30:15+01:00

Answer: [tex]\dfrac{25}{56}[/tex]

Step-by-step explanation:

Given: P(dot sent) = [tex]\dfrac37[/tex]

and P(dash sent) = [tex]\dfrac47[/tex]

P(dot received) = P(dot received ∩ dot sent)

+ P(dot received ∩ dash sent)

= P(dot received | dot sent)P(dot sent) + P(dash received | dash sent)P(dash sent) [By conditional probability formula]

[tex]=\dfrac78\times\dfrac37+\dfrac18\times\dfrac47=\dfrac{25}{56}[/tex]

Hence, the probability that the received symbol is a dot = [tex]\dfrac{25}{56}[/tex]