6. The values of the two variables \(A\) and \(B\) given in the table in Question 5 are written on cards and placed in two separate packs, which are labelled \(A\) and \(B\). One card is selected from Pack A. Let \(A _ { i }\) represent the event that the first digit on this card is \(i\).

1. Write down the value of \(\mathrm { P } \left( A _ { 2 } \right)\). The card taken from Pack \(A\) is now transferred into Pack \(B\), and one card is picked at random from Pack \(B\). Let \(B _ { i }\) represent the event that the first digit on this card is \(i\).
2. Show that \(\mathrm { P } \left( A _ { 1 } \cap B _ { 1 } \right) = \frac { 1 } { 24 }\).
3. Show that \(\mathrm { P } \left( A _ { 6 } \mid B _ { 5 } \right) = \frac { 4 } { 41 }\).
4. Find the value of \(\mathrm { P } \left( A _ { 1 } \cup B _ { 3 } \right)\).