Question

I need to find the probability and rounded to the third decimal place

Answer 1

Total cases = 7759

Total malfunctions caused by firmware = 456

Malfunctions due to other causes = 7759 - 456 = 7303

The probability that the firmware in the entire batch will be accepted =

`\begin{gathered} 3C_3((456)/(7759))^0((7303)/(7759))^3 \\ \\ =0.941229^3 \\ =0.83384 \\ \approx0.834\text{ (3 decimal places)} \\ \\ \text{ Since the probability is 0.834, which is close to 1, }The\text{ procedure is likely to result } \\ \text{ in }the\text{ entire batch being accepted} \end{gathered}`