Question

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​)?

Answer 1

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.