Question

I wrote a letter to my friend X and gave it to my son to post it. The probability that my son will forget to post the letter is $1/10$ and the letter will be lost in the post in $1/100$. If my friend X did not receive the letter, then the probability that

• A. my son forgot to post the letter is $891/1000$
• B. the letter was lost in the post $891/991$
• C. my son forgot to post the letter is $100/991$
• D. none of these

Answer 1

Answer: (A), (B)

The correct options are
A my son forgot to post the letter is $891/1000$
B the letter was lost in the post $891/991$

Probability that son will forget to post $=\frac{1}{10}$

Probability that letter will post the letter $=\frac{9}{10}$

Probability of the letter lost in post $=\frac{1}{100}$

Probability of the letter not lost in post $=\frac{99}{100}$

The friend did not receive the letter :

$\Rightarrow$ Case $1:$

The son forgot to post the letter $=P($son post the letter $)\times P($ letter not lost in post $)$

$=\frac{9}{10}\times \frac{99}{100}$

$=\frac{891}{1000}$

$\Rightarrow$ Case $2:$

Probability of letter lost in post $=\frac{P\left(letterforgottenbyson\right)}{1-P\left(letterpostedbyson\right)}$

$=\frac{\left(\frac{891}{1000}\right)}{1-\left(\frac{9}{1000}\right)}$

$=\frac{891}{991}.$

Hence, the answer is the letter was lost in the post $\frac{891}{991}.$