The probability of an outstanding student pass a biology test is 60%. If he takes three test, which are the experimental results for each test?
My doubt is if I should consider the pass=.6 since the first event or when it mentions that the probability is .6 and he takes three test, it's means that at the end of the third event is only when the pass=.6. In this second approach I should presume that in the first 2 attempts, the student pass score is 100%. Which is the correct approach?
Assuming the tests are independent (different tests) the probability of passing each is .6.
The probability of failing all three is .4^3
so the probability of passing at least one is
1 - .4^3
The correct approach depends on the specific details mentioned in the question. If it states that the probability of the outstanding student passing a biology test is 60%, it generally implies that the probability applies to each test independently. In this case, each test is considered a separate event, and the probability of passing remains constant at 60% for all three tests.
Using this approach, the student has a 60% chance of passing each individual test, and you can calculate the experimental results for each test separately. Here's how you can do it:
1. Test 1: Since the probability of passing the test is 60%, the probability of not passing (failing) is 1 - 0.6 = 0.4. Therefore, there is a 40% chance of failing the first test.
2. Test 2: Similarly, the probability of passing the second test is also 60%, and the probability of failing is 1 - 0.6 = 0.4. So, there is a 40% chance of failing the second test as well.
3. Test 3: Again, the probability of passing the third test is 60%, and the probability of failing is 1 - 0.6 = 0.4. Thus, there is a 40% chance of failing the third test.
Based on this approach, the experimental results for each test would suggest that there is a 60% chance of passing and a 40% chance of failing for all three tests.
It's essential to consider the context and wording of the question to determine if the probability applies to each test independently or only to the cumulative result after all three tests. If the question is unclear, you could seek clarification from the source or teacher to avoid any confusion.