A group of applicants for a position consists of 8 people who are qualified and 7 whoa are not. If we select two people at random to be interviewed (obviously without replacement), find the probability that we get:
a. two qualified people
b. one qualified and one unqualified person (think about different ways this could happen).
c. At least ONE qualified person. Hint: Use the complement law.
for a)i got the answer 4/15. 8/15*7/14
for b) i got the same answer
for c) the prob of picking both unqualified is 7/15*6/14= 1/5 so using complement would mean that i would take 1-1/5 to get 4/5???
The first two answers are right.
For C, to get "At least ONE qualified person," you want the probability for one qualified person plus the probability for two qualified persons.
I hope this helps. Thanks for asking.
Your answers for parts (a) and (b) are correct. Let's go through the calculations:
a) To find the probability of selecting two qualified people, we need to compute the probability of selecting one qualified person first, and then multiply it by the probability of selecting another qualified person from the reduced pool. The probability of selecting the first qualified person is 8/15 (because there are 8 qualified out of the total of 15 applicants). After one qualified person is selected, there are now 7 qualified people remaining out of a reduced pool of 14 applicants. So, the probability of selecting a second qualified person is 7/14. Therefore, the probability of selecting two qualified people is (8/15) * (7/14) = 4/15.
b) To find the probability of selecting one qualified and one unqualified person, we can consider the different ways this could happen. We could select a qualified person first and then an unqualified person, or we could select an unqualified person first and then a qualified person. The probability of selecting a qualified person first and then an unqualified person is (8/15) * (7/14) = 4/15 (which is the same as part (a)). Similarly, the probability of selecting an unqualified person first and then a qualified person is (7/15) * (8/14) = 4/15. So, the probability of selecting one qualified and one unqualified person is 4/15 + 4/15 = 8/15.
c) To find the probability of at least one qualified person, we need to consider the complement of the event where both people selected are unqualified. You correctly calculated the probability of selecting both unqualified people as (7/15) * (6/14) = 1/5. Therefore, the probability of at least one qualified person is equal to 1 minus the probability of selecting both unqualified people, which is 1 - 1/5 = 4/5.
Well done on your calculations for parts (a) and (b) and your application of the complement law in part (c)!