Barcallica 2 Report post Posted September 1, 2014 A die is rolled until a 6 occurs. What is the average total number of spots seen on the die before 6 occurs. For example 1,5,2,6 then the number is 1+5+2+6=14. Quote Share this post Link to post Share on other sites
0 witzar 18 Report post Posted September 1, 2014 Six tosses are needed on average to get a 6. Each of the first five tosses gives (1+2+3+4+5)/5 = 3 spots on average, plust 6 spots on last toss, so total 5*3 + 6 = 21 spots on averate are expected. Quote Share this post Link to post Share on other sites
0 DeGe 9 Report post Posted September 2, 2014 Nice Witzar. I had another approach which was to consider any expected dot rather than only 6... Since the expected number is also added, the expected number of dots would be same for any number from 1 to 6. Probability of each is 1/6 That means in 6 tosses all the numbers appear once (expected)... therefore, total dots = 1 + 2 + 3 + 4 + 5 + 6 = 21 This means that not counting the last dot, the expected numbers of dots for 1 to 6 are 20,19,18,17,16,15 respectively! Quote Share this post Link to post Share on other sites
0 Barcallica 2 Report post Posted September 2, 2014 Six tosses are needed on average to get a 6. Each of the first five tosses gives (1+2+3+4+5)/5 = 3 spots on average, plust 6 spots on last toss, so total 5*3 + 6 = 21 spots on averate are expected. Nice Witzar. I had another approach which was to consider any expected dot rather than only 6... Since the expected number is also added, the expected number of dots would be same for any number from 1 to 6. Probability of each is 1/6 That means in 6 tosses all the numbers appear once (expected)... therefore, total dots = 1 + 2 + 3 + 4 + 5 + 6 = 21 This means that not counting the last dot, the expected numbers of dots for 1 to 6 are 20,19,18,17,16,15 respectively! Both are valid solution Quote Share this post Link to post Share on other sites
A die is rolled until a 6 occurs. What is the average total number of spots seen on the die before 6 occurs. For example 1,5,2,6 then the number is 1+5+2+6=14.
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