A box contains 20 widgets, 4 of which are defective. If 4 are sold at random, find the probability that (a) all aredefective (b) none are defective.
A) $\frac { 1 } { 4845 } ; \frac { 364 } { 969 }$
B) $\frac { 1 } { 5 } ; \frac { 4 } { 5 }$
C) $\frac { 1 } { 116,280 } ; \frac { 1 } { 29,070 }$
D) $\frac { 1 } { 20 } ; \frac { 1 } { 5 }$

Question

A box contains 20 widgets, 4 of which are defective. If 4 are sold at random, find the probability that (a) all aredefective (b) none are defective. 
A) $\frac { 1 } { 4845 } ; \frac { 364 } { 969 }$
B) $\frac { 1 } { 5 } ; \frac { 4 } { 5 }$
C) $\frac { 1 } { 116,280 } ; \frac { 1 } { 29,070 }$
D) $\frac { 1 } { 20 } ; \frac { 1 } { 5 }$

Quizplus · Accepted Answer

The probability of all 4 widgets being defective is calculated using combinations: $\frac{{\binom{4}{4}\binom{16}{0}}}{{\binom{20}{4}}} = \frac{1}{4845}$. The probability of none being defective is $\frac{{\binom{4}{0}\binom{16}{4}}}{{\binom{20}{4}}} = \frac{364}{969}$.

A Box Contains 20 Widgets, 4 of Which Are Defective 14845;364969\frac { 1 } { 4845 } ; \frac { 364 } { 969 }48451​;969364​

A Box Contains 20 Widgets, 4 of Which Are Defective $\frac { 1 } { 4845 } ; \frac { 364 } { 969 }$