An urn contains 6 red, 4 blue, and 5 green balls. Two balls are drawn successively without replacement. What is the probability that both balls drawn are red?

Step-by-step solution

1. There are $6+4+5=15$ balls in total.
2. Probability the first ball is red $=6/15$ because 6 red out of 15.
3. After removing one red ball, 5 red remain and total balls left are $15-1=14$.
4. Probability the second ball is red $=5/14$.
5. Since the draws are dependent, multiply the two probabilities: $(6/15)\times (5/14)=30/210=1/7$.
6. So the required probability is $1/7$.

Concept tested: Probability of dependent events

Published 14 September 2026 · Last updated 16 September 2026 · How this solution was prepared and checked