A bag contains 3 red, 7 green and 4 yellow balls. Four balls are drawn together at random. What is the probability that at least 3 of the four balls are yellow?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(\frac{41}{1001}\)
“At least 3 yellow” means exactly 3 yellow or all 4 yellow. Count each case with combinations and add.
Total balls \(=3+7+4=14\); ways to draw 4 \(\displaystyle ={}^{14}C_4=\frac{14\times13\times12\times11}{24}=1001\)
Exactly 3 yellow and 1 of the other 10 balls \(={}^{4}C_3\times{}^{10}C_1=4\times10=40\)
All 4 yellow \(={}^{4}C_4=1\)
Favourable \(=40+1=41\)
Probability \(\displaystyle =\frac{41}{1001}\)