The bag contains:
- Red balls: 3
- Blue balls: 2
- Green balls: 5
- Yellow balls: 4
Total balls:
3+2+5+4=14
The total number of ways to pick 2 balls from 14 balls:
C(14,2)=214×13
=2182
=91
For both balls to be red, the number of ways to pick 2 red balls from 3 red balls:
C(3,2)=23×2=3
For both balls to be blue, the number of ways to pick 2 blue balls from 2 blue balls:
C(2,2)=1
Total favorable outcomes:
3+1=4
The probability that either both are red or both are blue:
P=Total outcomesFavorable outcomes
=914
Therefore, the probability is 914.