Probability Question
- Thread starter Kiana
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Steven G
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What have you tried? It is hard to help you on a math help forum if we do not know what you need help with. So please post back
You need to count.
How many different numbers can we have for _57?
How many different numbers can we have for 3_9?
Of all the combinations, how many have the top number bigger?
You need to count.
How many different numbers can we have for _57?
How many different numbers can we have for 3_9?
Of all the combinations, how many have the top number bigger?
Hi! I guess what I need help with is just knowing where to start the question or knowing how to start the question.
Steven G
Elite Member
- Joined
- Dec 30, 2014
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- 14,603
You marked this solved so I will post my solution.
_57 : 157, 257, 357, 457, 557, 657, 757, 857, 957
3_9: 309, 319, 329, 339, 349, 359, 369, 379, 389, 399
There are 9 numbers from _57 and 10 from 3_9. Therefore there are 9*10 or 90 combinations to check
If in _57 we place a 4,5,6,7,8 or 9 in the front position each of the 6 numbers will be larger than each of the 10 numbers from 3_9. So 60 numbers are lager for the top number.
If in _57 we place a 1 or 2 in the front position each of the 2 numbers will be smaller than each of the 10 numbers from 3_9. So 20 numbers are larger for the bottom number.
If we place a 3 in _57, resulting in 357, then 357 will be smaller if we place a 5,6,7,8 or 9 in the 2nd position of 3_9 and 357 will be larger if we place a 0,1,2,3 or 4 in 3_9. So 5 larger and 5 smaller.
Note that we did get 90 results: 60+20+5+5.
In 65 cases the top number was larger. So the probability that the top number is larger is 65/90 or 13/18.
This is an example of a problem where you need to get your hands dirty and just look at the cases.
_57 : 157, 257, 357, 457, 557, 657, 757, 857, 957
3_9: 309, 319, 329, 339, 349, 359, 369, 379, 389, 399
There are 9 numbers from _57 and 10 from 3_9. Therefore there are 9*10 or 90 combinations to check
If in _57 we place a 4,5,6,7,8 or 9 in the front position each of the 6 numbers will be larger than each of the 10 numbers from 3_9. So 60 numbers are lager for the top number.
If in _57 we place a 1 or 2 in the front position each of the 2 numbers will be smaller than each of the 10 numbers from 3_9. So 20 numbers are larger for the bottom number.
If we place a 3 in _57, resulting in 357, then 357 will be smaller if we place a 5,6,7,8 or 9 in the 2nd position of 3_9 and 357 will be larger if we place a 0,1,2,3 or 4 in 3_9. So 5 larger and 5 smaller.
Note that we did get 90 results: 60+20+5+5.
In 65 cases the top number was larger. So the probability that the top number is larger is 65/90 or 13/18.
This is an example of a problem where you need to get your hands dirty and just look at the cases.
Hi! Thank you so much for this it really helped a lot!
