A bag contains 3 red, 2 blue, 5 green and 4 yellow balls. If two balls are picked at random, what is the probability that either both are red or both are blue?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 4/91
The probability is the number of favourable pairs divided by the number of all possible pairs. “Both red” and “both blue” cannot happen together, so their favourable pairs are added.
Balls in the bag: \(3+2+5+4=14\)
All pairs: \({}^{14}C_{2}=\displaystyle\frac{14\times13}{2}=91\)
Both red: \({}^{3}C_{2}=3\) pairs
Both blue: \({}^{2}C_{2}=1\) pair
Probability \(\displaystyle =\frac{3+1}{91}=\frac{4}{91}\)