Repeated-number cards and an added value

Core stretch

Each object in the stated selection population is equally likely to be selected.

Nine cards show 3, 3, 3, 5, 5, 8, 10, 13 and 14.

1. One card is selected.
   1. Which number has probability \(\frac{1}{3}\)?[1]
   2. Find the probability of a prime.[2]
   3. Find the probability that the number is smaller than at least four numbers on the other cards.[2]
2. A tenth card labelled \(p<14\) is added and the probability of an odd number becomes \(\frac{3}{5}\). Find the largest possible integer \(p\).[2]