I have a few queries.Could you pls tell me the answer for the following questions?
1) Two dice are rolled, probability of getting 4 exactly once?
A) Using sample space, the answer is 5/18 but what is wrong in the answer 1/3 i.e 3 cases – either one 4, two 4’s or no 4’s. What am i missing here?
2) Reg. the dice sum in your Sleight of Mind 2 post, i referred all of your previous posts on upper limits but couldn’t figure out what values were missed during 19C3-4*13C3 that needed to be added with 6*7C3. Could you please elaborate?
Jan, in Q1, the three cases are not equiprobable. Tell me, if there are 100 people in a room, 99 girls and 1 boy. You select a student at random. What is the probability that it is a boy? According to your logic it should be 1/2!
In the 2nd query, it is not that they were missed but that they were double counted during the first subtraction. Suppose I subtracted the cases where a crossed 6. Then I subtracted the cases where b crossed 6. now in that, the cases where both crossed 6 simultaneously have been subtracted twice, and hence need to be added back. If possible, look up the “inclusion-exclusion principle” and the theory of Venn diagrams and sets (n(AUBUC) formula and so on) – perhaps at some future date I will put up a post on those.
Your repertoire of books is amazing… Thank you Sir for making CAT 2013 such an exciting journey through your blog… i m always eager check out the blog as soon as i start the computer… become a habit now…
9 days to go for the exam…
Thanks Girish, I shall be eagerly awaiting news from you on Jan 14 😉 Make the most of these 9 days (or rather 8 days now!) and remember to be calm and confident and relaxed. CAT is not as scary as people believe…:)
CAT-holics 
Dear J,
I have a few queries.Could you pls tell me the answer for the following questions?
1) Two dice are rolled, probability of getting 4 exactly once?
A) Using sample space, the answer is 5/18 but what is wrong in the answer 1/3 i.e 3 cases – either one 4, two 4’s or no 4’s. What am i missing here?
2) Reg. the dice sum in your Sleight of Mind 2 post, i referred all of your previous posts on upper limits but couldn’t figure out what values were missed during 19C3-4*13C3 that needed to be added with 6*7C3. Could you please elaborate?
Jan
Jan, in Q1, the three cases are not equiprobable. Tell me, if there are 100 people in a room, 99 girls and 1 boy. You select a student at random. What is the probability that it is a boy? According to your logic it should be 1/2!
In the 2nd query, it is not that they were missed but that they were double counted during the first subtraction. Suppose I subtracted the cases where a crossed 6. Then I subtracted the cases where b crossed 6. now in that, the cases where both crossed 6 simultaneously have been subtracted twice, and hence need to be added back. If possible, look up the “inclusion-exclusion principle” and the theory of Venn diagrams and sets (n(AUBUC) formula and so on) – perhaps at some future date I will put up a post on those.
regards
J
Your repertoire of books is amazing… Thank you Sir for making CAT 2013 such an exciting journey through your blog… i m always eager check out the blog as soon as i start the computer… become a habit now…
9 days to go for the exam…
Thanks Girish, I shall be eagerly awaiting news from you on Jan 14 😉 Make the most of these 9 days (or rather 8 days now!) and remember to be calm and confident and relaxed. CAT is not as scary as people believe…:)
regards
J