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

Answer:

(a)0.0005

(b)0.2720

Step-by-step 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) $=\dfrac{4}{16} \times \dfrac{3}{15} \times \dfrac{2}{14} \times \dfrac{1}{13}$

=0.0005

(b)Probability that  none are defective

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

P(none are defective) $=\dfrac{12}{16} \times \dfrac{11}{15} \times \dfrac{10}{14} \times \dfrac{9}{13}$

=0.2720