For the comprehensive final exam in MSDS 410, a student determines that the probability of passing the test with a B or better is 0.75. What are the odds of a student passing this test compared to not passing the test?

Question

For the comprehensive final exam in MSDS 410, a student determines that the probability of passing the test with a B or better is 0.75.  What are the odds of a student passing this test compared to not passing the test?

BlackTom AI · Accepted Answer

First, restating the scenario helps ground our reasoning: we are told the probability of passing the test with a B or better is 0.75, and we are asked for the odds of passing versus not passing.
To connect probability to odds, recall that odds in favor are defined as p:(1-p), where p is the probability of the event occurring.
Option A: 3:1. This corresponds to odds in favor of passing being 3 to 1. Translating back to probability, p = odds/(odds+1) = 3/(3+1) = 3/4 = 0.75, and the complementary probability (not passing) is 1 - p = 0.25. Indeed, 0.75 is the given passing probability, so 3:1 matches the correct odds.
Option B: 3:4. If the odds were 3:4, then p = 3/(3+4) = 3/7 ≈ 0.4286, which does not equal 0.75. This option misrepresents the relationship between odds and probability.
Option C: 1:3. Here p = 1/(1+3) = 1/4 = 0.25, implying a 25% chance to pass, not 75%. This is the opposite of the given information and therefore incorrect.
Option D: 4:3. With odds 4:3, p = 4/(4+3) = 4/7 ≈ 0.571, which differs from 0.75. This shows a miscalculation of the ratio needed to reach 0.75.
Option E: 1:1. Odds of 1:1 yield p = 1/(1+1) = 0.5, meaning a 50% chance to pass, not 75%. This option fails to reflect the provided probability.
In summary, by converting each odds ratio to the corresponding probability, only 3:1 yields the required 0.75 passing probability and the 0.25 not-passing probability, matching the given data.

For the comprehensive final exam in MSDS 410, a student determines that the probability of passing the test with a B or better is 0.75. What are the odds of a student passing this test compared to not passing the test?Single choice

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