I'm having trouble figuring out counting for probability questions. It seems that every problem I encounter is different and there's no algorithm to apply. As a result I can never really figure out how I'm supposed to apply formula's. This homework question I'm having trouble with is case in point, and perhaps someone could tell me where I keep going wrong with picking my counting technique.
In the Daily4 game, four numbers between 0 and 9 will be drawn in succession (repetitions allowed). The player marks four numbers on a game card and has a choice of how to play, straight (the player's numbers will match the four numbers drawn in exact order) or box (the player's numbers will match the four drawn in any order).
a. What is the size of the sample space? 10^4 = 10,000
b. what is the probability of a straight? 1/10,000 = 0.0001
I'm not understanding what I'm doing wrong here
c. What is the probability of a box if four distinct numbers are drawn?
4 distinct numbers = 10*9*8*7 = 5040
4 permutations of a "box" = 4P4 = 4
4/5040 = 1/1260 <-- I know this is wrongAnother way of doing the same problem:
each number is distinct: 10C4 = 210
1 combination of winning "box" = 1/210 <-- I'm also sure this is wrong
d. What is the probability of a box if two of the numbers drawn are the same?
pick 3 numbers, the remaining number has to be 1 of the 3 already picked.
10*9*8*3 = 2160
4 permuations of winning "box" = 4/2160 = 1/540
Thanks for your help!
In the Daily4 game, four numbers between 0 and 9 will be drawn in succession (repetitions allowed). The player marks four numbers on a game card and has a choice of how to play, straight (the player's numbers will match the four numbers drawn in exact order) or box (the player's numbers will match the four drawn in any order).
a. What is the size of the sample space? 10^4 = 10,000
b. what is the probability of a straight? 1/10,000 = 0.0001
I'm not understanding what I'm doing wrong here
c. What is the probability of a box if four distinct numbers are drawn?
4 distinct numbers = 10*9*8*7 = 5040
4 permutations of a "box" = 4P4 = 4
4/5040 = 1/1260 <-- I know this is wrongAnother way of doing the same problem:
each number is distinct: 10C4 = 210
1 combination of winning "box" = 1/210 <-- I'm also sure this is wrong
d. What is the probability of a box if two of the numbers drawn are the same?
pick 3 numbers, the remaining number has to be 1 of the 3 already picked.
10*9*8*3 = 2160
4 permuations of winning "box" = 4/2160 = 1/540
Thanks for your help!