I'm working on my last weak area before I am going to take the GMAT: PROBABILITY AND COMBINATORICS. So I apologize in advance if some of the questions I'm going to ask you guys are too easy.
QST: In a box with 10 blocks, 3 of which are red, what is the probability of picking a red block on each of your first two tries? Assume that you do NOT replace the first block after you have picked it.
ANS: I'm aware of the traditional way to solve problems like this (probability trees). By doing so, the answer is 3/10 * 2/9 = 1/15. Pretty straight forward.
Now, I want to also be able to solve this kind of problem with a counting method (combinatorics). So I thought I can solve it like this:
Unfortunately, I get the wrong result (2/15). This is double the OA (1/15). Any idea how to use the combination formula correctly in this scenario?
Total # of favorable outcomes: 2 red block out of three: 3C2=3
Total # of outcomes: any 2 blocks out of 10: 10C2=45
If you are putting in denominator the number of selections of 2 out of 10, you should also put in nominator number of selections of 2 out of 3.
# of selections of any first block out of 10=10C1, # of selection of any second out of 9=9C1=9, total 10C1*9C1=90
# of selections of the first red block out of three=3C1=3, # of selections of second red block out of three=2C1=2, total 3C1*2C1=6.
Hope it helps.
It would be better to post the questions in PS or DS forums to get more and quick replies.
NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!
PLEASE READ AND FOLLOW: 11 Rules for Posting!!!
RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;
COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat
DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests?
25 extra-hard Quant Tests
GMAT Club Premium Membership - big benefits and savings