Question

A box containing $100$ transistors $20$ of which are defective. From this box, $10$ transistors are drawn for inspection. What is the probability that (i) all $10$ are defective? (ii) all $10$ are good? (iii) at least one is defective? (iv) at most $3$ are defective?

Answer 1

100 transistors

20 defective transistor

i)Probability that 10 are defective $=\frac{{{20}_C}_{10}}{{{100}_C}_{10}}$

ii)Probability that 10 are good $=\frac{{{80}_C}_{10}}{{{100}_C}_{10}}$

iii)Probability that at most 3 are defective =P(0 defective)+P(1 defective)+P(2 defective)+P(3 defective)

$=\frac{{{80}_C}_{10}}{{{100}_C}_{10}}$$+\frac{{{80}_C}_9\times {{20}_C}_1}{{{100}_C}_{10}}+\frac{{{80}_C}_8\times {{20}_C}_2}{{{100}_C}_{10}}+\frac{{{80}_C}_7\times {{20}_C}_3}{{{100}_C}_{10}}$