In a certain experiment, there are three possible outcomes: R, S, and T. The probability that outcome R will occur is 0.48, and the probability that outcome S will occur is 0.36. If the experiment is repeated 250 ×, how many × would outcome T be expected to occur?

Rationale

Outcome T is expected to occur 40 times in 250 repetitions of the experiment.

To find the expected occurrences of outcome T, we first calculate the probability of T by subtracting the probabilities of outcomes R and S from 1. This gives us 1 - (0.48 + 0.36) = 0.16. Multiplying this probability by the total number of repetitions (250) results in an expectation of 40 occurrences for outcome T.

A (40) CORRECT

This choice represents the correct calculation. The probability of outcome T is 0.16, so in 250 trials, the expected occurrences are 250 × 0.16 = 40.

B (50) YOUR ANSWER

This choice incorrectly assumes a higher probability for outcome T. If T were to occur 50 times, that would imply a probability of 50/250 = 0.20, which exceeds the calculated probability of 0.16 based on the probabilities of outcomes R and S.

C (65) YOUR ANSWER

Choosing 65 for outcome T indicates a miscalculation of its probability. This would suggest a probability of 65/250 = 0.26, which contradicts the derived probability of 0.16. Therefore, this outcome is not feasible given the probabilities of R and S.

D (75) YOUR ANSWER

Selecting 75 implies an even greater probability of occurrence for outcome T, equating to 75/250 = 0.30. This value again exceeds the calculated probability of 0.16, making it an impossible outcome based on the probabilities provided for R and S.

Conclusion

The expected occurrences of outcome T is determined by first calculating its probability based on the known probabilities of R and S. With a probability of 0.16, it is anticipated to occur 40 times across 250 trials. The other options represent incorrect calculations, exceeding the valid thresholds established by the probabilities of the other outcomes.

In a certain experiment, there are three possible outcomes: R, S, and T. The probability that outcome R will occur is 0.48, and the probability that outcome S will occur is 0.36. If the experiment is repeated 250 ×, how many × would outcome T be expected to occur?

Outcome T is expected to occur 40 times in 250 repetitions of the experiment.

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