2025 CGS PRELIMS P2 Q2

A company conducted a survey in a girl’s school and found that a user’s likelihood of logging into a particular app each day depends on whether she logged in the previous day.

If the user logs in on a particular day, the probability that she logs in again the following day is 0.7. If the user does not log in on a particular day, the probability that she continues not logging in the next day is 0.8.

It is given that Emily logs in on Monday.

1. Find the probability that Emily logs in on Tuesday, Wednesday and Thursday.[2]
2. Find the probability that Emily does not log in on Wednesday.[2]
3. Each time the user logs in, she will earn 10 reward points. If the user does not log in, no reward points will be given.
   1. Find the probability that Emily earns exactly 20 points by Wednesday.[2]
   2. Find the probability that Emily earns more than 10 points by Wednesday.[2]