Final answer:
Given the experiment's historical success rate from the original 1,271 trials, where it failed 435 times, the expected number of failures in 732 trials is calculated as 251 when rounded to the nearest whole number.
Step-by-step explanation:
To calculate the expected number of failures in 732 trials, based on the experiment's historical success rate, we can use the relative frequency of failure from the original 1,271 trials. First, we find out how many times the experiment failed in the original set.
Total trials = 1,271
Successful trials = 836
Failed trials = Total trials - Successful trials
Failed trials = 1,271 - 836 = 435 failures
Next, we calculate the experimental probability of failure.
Probability of failure = Failed trials / Total trials
Probability of failure = 435 / 1,271
With the probability of failure known, we can estimate the expected number of failures in a new set of 732 trials.
Expected failures in 732 trials = Probability of failure * New trials
Expected failures = (435 / 1,271) * 732
When you calculate this, you get an expected number of failures of approximately 250.68, which we'll round to the nearest whole number:
Expected failures ≈ 251 (rounded)
Therefore, the expected number of failures given 732 trials is approximately 251.