Question

among 9938 cases of heart pacemaker malfunctions, 577 were found to be caused by firmware, which is software programmed into the device. if the firmware is tested in 3 different pacemakers randomly selected from this batch of 9938 and the entire batch is accepted if there are no failures, what is the probability that the firmware in the entire batch will be accepted? is this procedure likely to result in the entire batch being accepted?
the probability is . this procedure is to result in the entire batch being accepted. (round to three decimal places as needed.)

Explanation:

Step1: Calculate non - failure rate for one pacemaker

The number of non - failure cases is $9938 - 577=9361$. The probability that a single pacemaker does not have a firmware - related failure is $p=\frac{9361}{9938}$.

Step2: Calculate probability for 3 non - failing pacemakers

Since the selections are independent, the probability that all 3 pacemakers do not have firmware - related failures is $P = (\frac{9361}{9938})^3$.
\[

$$\begin{align*} P&=(\frac{9361}{9938})^3\\ &=(\ 0.942\ )^3\\ &\approx0.836 \end{align*}$$

\]

Answer:

The probability is $0.836$. This procedure is likely to result in the entire batch being accepted.