A jar contains 8 large red marbles, 5 small red marbles, 7 large blue marbles, and 4 small blue marbles. if a marble is chosen at random, which of the conditional probabilities is larger, p (red |large ) or p (large |red ) ?

8 large red, 5 small red, 7 large blue, 4 small blue:

totally = 24 marbles

P (red) = 13/24

let A red and B large

P (A/B) = P (A∩B) / P (B)

P (B) = 15/24 =.625

P (A∩B) = 8/24 =.333

P (A/B) =.333/.625 =.533

P (B/A) =.625/.333 = 1.875

so the probability of p (large/red) is larger.