bonanova Posted January 24, 2008 Report Share Posted January 24, 2008 You have 3 baskets. Each basket contains 4 balls, indistinguishable except for color. There is a red, a white, a blue, and a black ball in each basket. You are blindfolded and asked to remove one ball from each basket. What are the chances you will pick exactly 2 red balls and 1 non-red ball? Quote Link to comment Share on other sites More sharing options...
0 Guest Posted January 24, 2008 Report Share Posted January 24, 2008 9/64 = 1/4 * 1/4 * 3/4 * 3 Red Red Non-red The number of baskets where the non-red ball can be pulled Quote Link to comment Share on other sites More sharing options...
0 Guest Posted January 24, 2008 Report Share Posted January 24, 2008 The long way is... R = Red, W = White, B = Blue, K = Black RRR rrw rrb rrk rwr RWW RWB RWK rbr RBW RBB RBK rkr RKW RKB RKK wrr WRW WRB WRK WWR WWW WWB WWK WBR WBW WBB WBK WKR WKW WKB WKK brr BRW BRB BRK BWR BWW BWB BWK BBR BBW BBB BBK BKR BKW BKB BKK krr KRW KRB KRK KWR KWW KWB KWK KBR KBW KBB KBK KKR KKW KKB KKK The lower case letters meet the criteria. 9/64 Quote Link to comment Share on other sites More sharing options...
0 Guest Posted January 25, 2008 Report Share Posted January 25, 2008 now let's change it... You are now asked to remove two balls from each basket (ie 6 balls total). Are you more likely to pick exactly [1 red ball and 5 non-red balls] or exactly [2 red balls and 4 non-red balls]? What are the chances? extra credit - anyone can run the options out the long way (I did ) - but can you explain the math behind the result? I left my high-school math way behind, so don't have a clue what the formula would look like... Quote Link to comment Share on other sites More sharing options...
0 bonanova Posted January 25, 2008 Author Report Share Posted January 25, 2008 Are you more likely to pick exactly [1 red ball and 5 non-red balls] or exactly [2 red balls and 4 non-red balls]? What are the chances?No. You're not more likely to pick 1 red ball or 2 red balls. The chances are 3/8 for both outcomes.Basically, if you pick 2 balls from a basket, half the time you'll get the red one [RW, RB, RK], and half the time you won't [WB, WK, BK]. Of the 8 outcomes of picking from three baskets, there are 3 ways to get 1 red [100 010 001], and 3 ways to get 2 red [110 101 011]. There are also 1/8 chances for 0 red [000] and 3 red [111]. Going a little slower, With regard to getting red balls when picking from all three baskets, there are 8 equally likely outcomes. You get 1 red ball in three of the outcomes and 2 red balls in three other outcomes: 0 0 0 = 0 red balls 1 0 0 = 1 red balls 0 1 0 = 1 red balls 0 0 1 = 1 red balls 1 1 0 = 2 red balls 1 0 1 = 2 red balls 0 1 1 = 2 red balls 1 1 1 = 3 red balls Probability of getting 0 red balls taking 2 from each basket = 1/8 Probability of getting 1 red balls taking 2 from each basket = 3/8 Probability of getting 2 red balls taking 2 from each basket = 3/8 Probability of getting 3 red balls taking 2 from each basket = 1/8 Quote Link to comment Share on other sites More sharing options...
Question
bonanova
You have 3 baskets.
Each basket contains 4 balls, indistinguishable except for color.
There is a red, a white, a blue, and a black ball in each basket.
You are blindfolded and asked to remove one ball from each basket.
What are the chances you will pick exactly 2 red balls and 1 non-red ball?
Link to comment
Share on other sites
4 answers to this question
Recommended Posts
Join the conversation
You can post now and register later. If you have an account, sign in now to post with your account.