51. 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?
Answer: A
Outcome T is expected to occur 40 times.
In the given experiment, the probabilities of outcomes R and S are 0.48 and 0.36, respectively. Therefore, the probability of outcome T is 1 - (0.48 + 0.36) = 0.16. When the experiment is repeated 250 times, outcome T would be expected to occur 0.16 × 250 = 40 times.
A) 40
This option correctly calculates the expected occurrences of outcome T by using the formula for probability. With a total of 250 trials and a probability of 0.16 for outcome T, the calculation yields 40 occurrences, making this option correct.
B) 50
Option B is incorrect as it suggests that outcome T would occur 50 times. This does not align with the calculated probability of 0.16, which would result in a significantly lower number of expected occurrences when multiplied by the total trials.
C) 65
Option C is also incorrect. The expected number of occurrences for outcome T, calculated from its probability, is much less than 65. This option misrepresents the distribution of probabilities among the three outcomes.
D) 75
This option is incorrect as well. A probability of 0.16 does not support an expectation of 75 occurrences of outcome T in 250 trials. This choice miscalculates the impact of the given probabilities on the total outcomes.
Conclusion
The correct answer of 40 occurrences for outcome T is derived directly from the probability calculations based on the provided probabilities of R and S. All other options fail to accurately reflect the expected value derived from the experiment's probability distribution, confirming the correctness of option A.