Using Bayes theorem what is the probability of dropping the call after 50sec given call was not dropped during first 20 sec.

Question

I have probabilities of dropping a call based on the duration of time customer has waited for before dropping.

Probability of dropping during 0-20sec: 0.23

Probability of dropping during 20-40sec: 0.11

Probability of dropping during 40-50sec: 0.04

Probability of dropping during 50-60sec: 0.61

Now I want to know the probability of dropping the call during 50-60sec when it is known that the call has not been dropped during 0-20sec.

How can we solve it using Bayes theorem ?

Answer 1

Simply

$$\frac{0.61}{1-0.23}=\frac{61}{77}$$

This simple operation is exactly Bayes Theorem, or Conditional Probability formula...it's the same

Set:

$A$ as the event: "dropping during 50-60sec"

$B$ the complement of the event "dropping during 0-20"

$$P(A|B)=\frac{P(A\cap B)}{P(B)}=\frac{P(A)}{P(B)}$$

being $A \subset B$