2 A bag contains 26 cards. A different letter of the alphabet is written on each one. A card is chosen at random and its letter is written down. The card is returned to the bag. The bag is shaken and the process is repeated several times. Tania wants to investigate the probability of a letter appearing twice. She wants to know how many cards need to be chosen for this probability to exceed 0.5. Tania uses the following algorithm. Step 1 Set \(n = 1\)
Step 2 Set \(p = 1\)
Step 3 Set \(n = n + 1\)
Step 4 Set \(p = p \times \left( \frac { 27 - n } { 26 } \right)\)
Step 5 If \(p < 0.5\) then stop
Step 6 Go to Step 3

1. Run the algorithm.
2. Interpret your results. A well-known problem asks how many randomly-chosen people need to be assembled in a room before the probability of at least two of them sharing a birthday exceeds 0.5 (ignoring anyone born on 29 February).
3. Modify Tania's algorithm to answer the birthday problem. (Do not attempt to run your modified algorithm.)
4. Why have 29 February birthdays been excluded?