Related to another thread: Here is another problem that is similar that I know the answers to and perhaps it will shed some light on the issue.
In the Daily3 game, three numbers between 0 and 9 will be drawn in succession (repetitions allowed). The player marks three numbers on a game card and has a choice of how to play, straight (the player's numbers will match the three numbers drawn in exact order) or box (the player's numbers will match the three drawn in any order).
a. What is the probability of a box if 3 distinct numbers are drawn? Answer: 0.006
I was initially thinking that "drawn" means the sample space was changing. For instance, instead of 10x10x10 for total possible combinations, it was 10x9x8. However now I notice that if I take it to mean that I "pick" 3 distinct numbers I get the right answer. 3P3 = 6 total permutations of 3 distinct numbers, 6/1000 = 0.006.
I'm not sure if I'm just accidentally arriving at the correct answer in the wrong way though.
b. what is the probability of a box if 2 of the numbers drawn are the same? Answer: 0.003
again if I use the same interpretation of the problem then I can arrive at the correct answer.
If I pick XXY as my 3 numbers, there are 3 distinct ways to order XXY
XXY
XYX
YXX
3/1000 = 0.003.
I'm not really sure how to do that ordering on part b more mathematically than just trial and error like that though, which is the problem I keep running into on tests.
I think the confusing part of this question was the use of the word "drawn", however I'm still not sure I'm interpreting it correctly.
Thanks for you help
In the Daily3 game, three numbers between 0 and 9 will be drawn in succession (repetitions allowed). The player marks three numbers on a game card and has a choice of how to play, straight (the player's numbers will match the three numbers drawn in exact order) or box (the player's numbers will match the three drawn in any order).
a. What is the probability of a box if 3 distinct numbers are drawn? Answer: 0.006
I was initially thinking that "drawn" means the sample space was changing. For instance, instead of 10x10x10 for total possible combinations, it was 10x9x8. However now I notice that if I take it to mean that I "pick" 3 distinct numbers I get the right answer. 3P3 = 6 total permutations of 3 distinct numbers, 6/1000 = 0.006.
I'm not sure if I'm just accidentally arriving at the correct answer in the wrong way though.
b. what is the probability of a box if 2 of the numbers drawn are the same? Answer: 0.003
again if I use the same interpretation of the problem then I can arrive at the correct answer.
If I pick XXY as my 3 numbers, there are 3 distinct ways to order XXY
XXY
XYX
YXX
3/1000 = 0.003.
I'm not really sure how to do that ordering on part b more mathematically than just trial and error like that though, which is the problem I keep running into on tests.
I think the confusing part of this question was the use of the word "drawn", however I'm still not sure I'm interpreting it correctly.
Thanks for you help
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