Question

Among 16 electrical components exactly 4 are known not to function properly. If 6 components are randomly selected, find the following probabilities: (i) The probability that all selected components function properly. (ii) The probability that exactly 3 are defective. (iii) The probability that at least 1 component is defective.

Answer 1

Given that the number of electrical components is 16

number of components not working =4

number of components working=16-4=12

In the question we are selecting 6 components randomly

So the number of ways of selecting 6 components from 16 components is   

(i)The probability that all selected components function properly?

we require all components functional in this question so now we have to select the components from the working components.

the number of ways of selecting 6 components from the working components=

  

The probability that all selected components function properly=

=924/8008

=0.1153

(ii) The probability that exactly 3 are defective

as we need exactly 3 components from 4 defective

the number of ways of selecting 3 from 4 defectives==4C3=4!/3!*1!=4

the number of ways of selecting other 3 from 12 working components ==220

the number of ways of selecting exactly 3 defectives =the number of ways of selecting 3 from 4 defectives * the number of ways of selecting other 3 from 12

=4 *220

=880

The probability that exactly 3 are defective=the number of ways of selecting exactly 3 defectives/ the number of ways of selecting 6 from 16 components

=880/8008

=0.1098

(iii)The probability that at least 1 component is defective =1-  The probability that all selected components function properly

=1-0.1153

=0.8847