Grades on a very large statistics course have historically been awarded according to the following distribution.

HD D C P Z or Fail
0.15 0.20 0.30 0.30 0.05

What is the probability that a student scores higher than a Credit (C)?

Question

Grades on a very large statistics course have historically been awarded according to the following distribution.

HD	D	C	P	Z or Fail
0.15	0.20	0.30	0.30	0.05

What is the probability that a student scores higher than a Credit (C)?

BlackTom AI · Accepted Answer

Higher than a Credit means the student must have a Distinction (D) or a High Distinction (HD), so we add the probabilities of those grades.

1. Relevant knowledge points and concepts
- Probabilities for mutually exclusive outcomes add: if events cannot happen simultaneously (a student cannot get both HD and D), P(HD or D) = P(HD) + P(D).
- Interpreting "higher than a Credit" excludes Credit itself; only grades strictly above C count.
- The distribution given represents long-run probabilities/frequencies for each grade.

2. Step-by-step reasoning
- Identify which categories are strictly above C: HD and D.
- Use the addition rule for mutually exclusive events to find the combined probability.

3. Calculations (all intermediate steps)
- P(HD) = 0.15
- P(D) = 0.20
- P(higher than C) = P(HD) + P(D) = 0.15 + 0.20
- 0.15 + 0.20 = 0.35

(Alternate check via complement: P(higher than C) = 1 − P(C or lower) = 1 − [P(C) + P(P) + P(Z)] = 1 − (0.30 + 0.30 + 0.05) = 1 − 0.65 = 0.35.)

4. Why the correct answer is correct
Because “higher than C” includes only the two mutually exclusive categories HD and D and their probabilities sum to 0.35. Both the direct sum and the complement calculation give the same result, confirming consistency.

5. Why other possible interpretations are incorrect
- Including C (i.e., “C or higher”) would give P = 0.30 + 0.20 + 0.15 = 0.65, which misreads “higher than.”
- Counting Pass (P) or Fail (Z) as “higher than C” is incorrect because those are lower or equal ranks than C.

Conclusion: The probability a student scores higher than a Credit is 0.35, which matches the provided answer.

Grades on a very large statistics course have historically been awarded according to the following distribution. HD D C P Z or Fail 0.15 0.20 0.30 0.30 0.05 What is the probability that a student scores higher than a Credit (C)?单项选择题

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