'A' writes a letter to his friend 'B' and gives it to his son to post it in a letter box, the reliability of his son being 3/4 . The probability that a letter posted will get delivered is 8/9 . At a later date, 'A' hears from 'B' that the letter has not reached him. Find the probability that the son did not post the letter at all .

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Please find below the solution to the asked query:

Let P  be the probabilty that son posts the letter.P=34Hence, probabilty that he does not post letter is given by:P¯=1-34=14Let Q be the probabilty that letter is delivered.Q=89Hence probability that letter is not delivered is given by:Q¯=1-89=19NowTotal probabilty that letter is not delivered to B=Probabilty that son does not post letter OR Son posts letter ANDletter is not deliveredTotal Probability=P¯+P×Q¯=14+34×19=14+112=412=13Probability that son did not post the letter at all=P¯Total Probability =1413=34 Answer

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