A box contains five coated and ten otherwise identical uncoated cutting inserts, randomly mixed. An operator takes four simultaneously for a four-tooth face mill without distinguishing them. Find the probability all four are uncoated (two decimals).
Sampling is without replacement. Favorable subsets number $\binom{10}4$, while all possible subsets number $\binom{15}4$. Thus $P=210/1365\approx0.153846$, giving **0.15**.
More Probability and Statistics questions
GATE 2026 PI Q61– Soldering-defect count per semiconductor device is Poisson with p(x)=e-x/x! and mean…
GATE 2025 PI Q15– A bag has five red, seven green and three blue balls. Two balls are drawn randomly one…
GATE 2025 PI Q58– Marketing expenditure x and annual profit y over three years are (3,22),(4,27),(6,36), in…
GATE 2024 PI Q31– A continuous variable has density f(x) = K/4 on 0 ≤ x ≤ 1, and zero otherwise. Find K…
GATE 2024 PI Q45– Seven mixed cards numbered 1–7 are in a box. One is drawn randomly and known to be odd.…
GATE 2023 PI Q14– Three unbiased coins are tossed. Given that at least two outcomes are tails, find the…