Question

Suppose a jar contains 14 red marbles and 38 blue marbles. If you reach in the jar and pull out 2 marbles at random at the same time, find the probability that both are red.

Answer 1

14 red marbels and 38 blue marbles,

Total marbles in Jar = 14 + 38 = 52,

2 marbles are selected at random,

Probability that both are red  $= \frac{^{14}C_2}{^{52}C_2}$

  $= \frac{\frac{14!}{2!12!}}{\frac{52!}{2!50!}}$

  $= \frac{\frac{13*14}{1*2}}{\frac{51*52}{1*2}}$

  $= \frac{182}{2652} = 0.0686$

Probability that both are red is 0.0686