There are a couple of ways to approach this question, depending on how comfortable you are with the math concepts involved. There's a great 'brute force' element to the question that you can take advantage of (as long as you write everything down and label your work).
We're told that we have a group of 8 people (some men and some women). We're told to randomly select 2 of the 8 people and we're asked if the probability that they're BOTH men is greater than .25 This is a YES/NO question.
Since there are only 8 people, we can have from 0 - 8 men in the group. We can do a bit of work up-front so that we can move faster through the two Facts later. We want to figure out the point at which the probability will be > .25
There are 4 men and 4 women
Probability of selecting 2 men is (4/8)(3/7) = 3/14
Since 3/12 = .25, 3/14 must be LESS than .25 (since the denominator of that fraction is bigger than 12)
There are 5 men and 3 women
Probability of selecting 2 men is (5/8)(4/7) = 5/14
Since 5/15 = .333333, 5/14 must be BIGGER than .3333 (since the denominator of that fraction is smaller than 15)
So, with 4 OR FEWER men, the answer to the question is NO
With 5 OR MORE men, the answer to the question is YES
We now know that the question is really asking if the number of men is 5 OR GREATER. Again, this is a YES/NO question.
Fact 1: MORE than 40% of the employees are men.
(.4)(8) = 3.2, BUT since we CANNOT have a "fraction" of a man, we must have 4 OR MORE men....
IF...we have 4 men, then the answer to the question is NO
IF...we have 5 men, then the answer to the question is YES
Fact 1 is INSUFFICIENT
(2) The probability that both the selected people will be women is more than 20%.
For this Fact, we can use the calculations that we did at the beginning (with a little extra work).
There are 4 women and 4 men
Probability of selecting 2 women is (4/8)(3/7) = 3/14
Since 3/15 = .2, 3/14 must be GREATER than .2 (since the denominator of that fraction is less than 15)
This tells us that we have 4 OR MORE women.
IF... we have 4 women, then the answer to the question is NO
IF... we have MORE women, we have even FEWER men and the answer to the question is still NO.
Fact 2 is SUFFICIENT
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