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

question 42

Multiple Choice

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) \(\frac { 1 } { 26 } ; \frac { 2 } { 13 }\)

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Definitions:

Phenotype Frequency

Phenotype frequency refers to the proportion of individuals in a population that exhibit a specific observable trait or phenotype.

Temporal Isolation

A prezygotic reproductive isolating mechanism in which genetic exchange is prevented between similar species because they reproduce at different times of the day, season, or year.

Genetic Exchange

The process by which genetic information is transferred between organisms, leading to variation in genetic makeup.

Diurnal Isolation

Diurnal isolation is a form of reproductive isolation where species may share the same habitat but are active at different times of the day, thus preventing mating.