Compute Probabilities Involving Permutations and Combinations
-A box contains 26 widgets, 4 of which are defective. If 4 are sold at random, find the probability that (a) all are defective (b) none are defective.
A) $\frac { 1 } { 14,950 } ; \frac { 1463 } { 2990 }$
B) $\frac { 2 } { 13 } ; \frac { 11 } { 13 }$
C) $\frac { 1 } { 358,800 } ; \frac { 1 } { 89,700 }$
D) $\frac { 1 } { 26 } ; \frac { 2 } { 13 }$

Question

Quizplus · Accepted Answer

The probability that all 4 widgets sold are defective is calculated using combinations: $\frac{{\binom{4}{4}}}{\binom{26}{4}} = \frac{1}{14,950}$. The probability that none are defective is calculated by choosing 4 out of the 22 non-defective widgets: $\frac{{\binom{22}{4}}}{\binom{26}{4}} = \frac{1463}{2990}$.

Compute Probabilities Involving Permutations and Combinations -A Box Contains 26 114,950;14632990\frac { 1 } { 14,950 } ; \frac { 1463 } { 2990 }14,9501​;29901463​

Compute Probabilities Involving Permutations and Combinations
-A Box Contains 26 $\frac { 1 } { 14,950 } ; \frac { 1463 } { 2990 }$