A drawer has 3 blue socks, 5 brown socks and 4 white socks. If two socks are picked together at random, what is the probability that both socks are of the same colour?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \(\frac{19}{66}\)
Picking two socks together is a selection, so the outcomes are counted with combinations. “Same colour” means both blue, or both brown, or both white, and these cases are added.
Total socks \(=3+5+4=12\); ways to pick 2 \(\displaystyle ={}^{12}C_2=\frac{12\times11}{2}=66\)
Both blue \(={}^{3}C_2=3\)
Both brown \(\displaystyle ={}^{5}C_2=\frac{5\times4}{2}=10\)
Both white \(\displaystyle ={}^{4}C_2=\frac{4\times3}{2}=6\)
Same colour \(=3+10+6=19\) ways
Probability \(\displaystyle =\frac{19}{66}\)