Question

Among 7 electrical components exactly one is known not to function properly. If 4 components are randomly selected, find the probability that all selected components function properly.

Answer 1

Answer: 0.4286

Step-by-step explanation:

Given : Total components = 7

Number of bad component  in 7 electrical components  = 1

Number of good component  in 7 electrical components = 7-1=6

The number of combinations of selecting any 4 components =  $^{7}C_4$

The number of combinations of selecting all 4 good components  = $^{6}C_4$

Then, the probability that all selected components function properly will be :

$\dfrac{^6C_4}{^7C_4}=\dfrac{\dfrac{6!}{4!(6-4)!}}{\dfrac{7!}{4!(7-4)!}}\\\\=\dfrac{\dfrac{6\times5\times4!}{4!2!}}{\dfrac{7\times6\times5\times4!}{4!\times3!}}\\\\=\dfrac{3}{7}\\\\\approx0.4286$

Hence, the probability that all selected components function properly. is 0.4286 .