Question

A sample of 4 different calculators is randomly selected from a group

containing 46 that are defective and 26 that have no defects. What is the
probability that all four of the calculators selected are defective? Round to four
decimal places.
A) 0.1021 B) 0.1586 C) 0.1666 D) 10.9154

Answer 1

`\displaystyle\\|\Omega|=\binom{72}{4}=(72!)/(4!68!)=(69\cdot70\cdot71\cdot72)/(2\cdot3\cdot4)=1028790\\|A|=\binom{46}{4}=(46!)/(4!42!)=(43\cdot44\cdot45\cdot46)/(2\cdot3\cdot4)=163185\\\\P(A)=(163185)/(1028790)=(473)/(2982)\approx0.1586`