Question

Sol. [Key Concept: Urn 20W+30B+50…: probability by counting.]

$A \rightarrow$ event that white balls are not among the 10 selected marbles.

B → event that blue balls are not among the 10 selected marbles.

$C \rightarrow$ event that red balls are not among the 10 selected marbles.

$$\begin{matrix} P(A \cup B \cup C) & \ = \left( \frac{80}{100} \right)^{10} + \left( \frac{70}{100} \right)^{10} + \left( \frac{50}{100} \right)^{10} - \left( \frac{50}{100} \right)^{10} - \left( \frac{30}{100} \right)^{10} - \left( \frac{20}{100} \right)^{10} \\ & \ = \frac{8^{10} + 7^{10} - 3^{10} - 2^{10}}{10^{10}} \end{matrix}$$