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 = [tex]^{7}C_4[/tex]
The number of combinations of selecting all 4 good components = [tex]^{6}C_4[/tex]
Then, the probability that all selected components function properly will be :
[tex]\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[/tex]
Hence, the probability that all selected components function properly. is 0.4286 .
