Test probability

Question

akili has two tests, the probabil that he will pass the first test is 3/4. How he does on the first test affects the second test. If he passes the first test there is a 4/5 chance that he will pass the second test. If he doesn't pass the first test then there is a 1/3 chance he will pass the second test. What is the chance he will pass exactly one test, Express the answer in fraction form,

Answer 1

The easiest way for me to explain this problem is by using a tree diagram. The first two limbs would be Pass (3/4) and Fail (1/4)[1/4 is obtained by subtracting 1 - 3/4 because the limbs should total 100%]. Next, split two limbs from Pass that have Pass (4/5) and Fail (1/5)[Same 100% rule here]. Next, split two limbs from  Fail that have Pass (1/3) and Fail (2/3)[100% rule].

Since you are only concerned with passing at exactly one test, on our tree this can occur with a pass 1st test/fail second test or fail 1st test/pass 2nd test. Use the multiplication rule on these two limbs and then add the solutions to get your probability of passing exactly 1 test. So, (3/4 times 1/5 = 3/20) for Pass/Fail and (1/4 times 1/3 = 1/12) for Fail/Pass. Add these two probabilities together (3/20 + 1/12 really is 9/60 + 5/60 or 14/60, which is simplified to 7/30).

Have a good one now,

Dr. P

Answer 2

Probability of passing the first test is 3/4.

 

If he fails the first test, then the probability of passing the second test is 1/3.

But the probability of failing the first test is 1/4. So the probability of these

events are 1/4*1/3 = 1/12

 

3/4 + 1/12 = 9/12 + 1/12 = 10/12 = 5/6 of passing one or the other