Question

Among 8850 cases of heart pacemaker malfunctions, 370 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 8850 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 (Round to three decimal places as needed.) to result in the entire batch being accepted.

Answer 1

The probability that the firmware in the entire batch will be accepted is approximately 0.953.

It is likely that this procedure will result in the entire batch being accepted.

The probability of this procedure resulting in the entire batch being accepted is approximately 0.953.

Step-by-step explanation:

To find the probability that the firmware in the entire batch will be accepted, we can use the concept of binomial probability.

The probability of acceptance for a single pacemaker is the complement of the probability of failure, which is 1 - (370/8850).

Since we are testing 3 pacemakers, the probability of all 3 being accepted is (1 - 370/8850)^3.

Using this formula, we can calculate the probability as follows:

P(all accepted) = (1 - 370/8850)^3

≈ 0.953

Therefore, the probability that the firmware in the entire batch will be accepted is approximately 0.953.

Likelihood of Entire Batch Acceptance

Given that the probability of acceptance for a single pacemaker is high at approximately 0.953, it is likely that this procedure will result in the entire batch being accepted.

Conclusion

The probability is high at approximately 0.953 to result in the entire batch being accepted.