Question

A box contains 16 ​transistors, 4 of which are defective. if 4 are selected at​ random, find the probability that

a. all are defective.

b. none are defective.

Answer 1

(a)0.0005

(b)0.2720

Explanation:

Total Number of Transistors = 16

To find the probability that 4 selected at random are defective (or non-defective), we find the probability of the 1st, 2nd, 3rd, and 4th defective (or non-defective) items in that order, Note that the selection is without replacement.

(a)Probability that all are defective

Number of Defective Transistors =4

P(all are defective)
`=(4)/(16) * (3)/(15) * (2)/(14) * (1)/(13)`

=0.0005

(b)Probability that none are defective

Number of Non-Defective Transistors =16-4=12

P(none are defective)
`=(12)/(16) * (11)/(15) * (10)/(14) * (9)/(13)`

=0.2720