HarveyKlaus wrote:

The table shows the distribution of a group of 40 college students by gender and class (in the pic), If one student is randomly selected from this group, find the probability that the student chosen is

(i) a male sophomore or a female senior

(ii) a female or a sophomore

My approach is:

(i) a male sophomore or a female senior

Sol: I divide the prompt in two section. the first is a male sophomore => 6 / 40 and the second part is a female senior => 3 / 40. Since its OR in-between these two categories, we add both after simplification => 3/20 + 3/40 ==> 9 / 40. And the answer is correct.

However, when I apply the same logic to the second prompt (ii) " a female or a sophomore "

Sol: First part --> Since there are overall 22 females in the whole population, the prob. of selecting a female would be 22 / 40 or 11 / 20. Secondly --> Since there are 16 sophomores in the whole population, the prob. of selecting a sophomore would be 16 / 40 or 2 / 5. Since there is OR in-between these two main categories, we add 11 / 20 + 2 / 5 ==> 19/20. BUT this is not the correct answer. (The correct answer is 28 / 40)

Problem: In the first prompt, my logic and the way I approach this problem works however, in the second prompt, it does not. What am I missing?

Thanks for your help!

H.

What you are missing is that there are female students who are sophomores and you are counting them twice while calculating your probability. So you can subtract the probability of females who are sophomores. In the first case, there is no intersection of a male sophomore and female senior i.e there won't be any male sophomore who would be a female senior as well.

Hope it helps