2022 EJC J2 MYE P2 Q9

\(16\%\) of all phone calls are scam calls. A company designed a \(2\)-stage filtering anti-scam app, \({{X}^{2}}\)scam, that can block scam calls which plague mobile phone users. In a pre-launch test, it is found that \({{X}^{2}}\)scam blocked \(88\%\) of calls that are scam calls and \(5\%\) of calls that are non-scam calls in the first stage of filtering. Of the calls that are unblocked in the first stage, \({{X}^{2}}\)scam blocks \(99\%\)of scam calls and \(5\%\) of non-scam calls within the second stage. Calls that are blocked in the first stage do not go through a second stage of filtering.

1. Draw a tree diagram to represent the above information.[2]

A call is selected at random. Find the probability that

2. it is a scam call that is blocked.[2]
3. it is a scam call, given that the call is blocked.[2]

Three calls were selected at random.

4. Find the probability that \({{X}^{2}}\)scam correctly filters exactly two of the calls.[4]