Post by: roshanajabbour on August 03, 2016, 04:28:14 pm
A three-digit number is selected from the numbers 3,4,5,7,8,9 with no repetition.
What is the probability that he number formed is greater than 800?
I've already figured out the first part of the answer and found that the total numbers formed was 6P3=120
Can i please get help with finding the rest?
Post by: RuiAce on August 03, 2016, 04:37:35 pm
Moderator action was an accident in misclicking. My bad :) overall I edited nothing.
Post by: studybuddy7777 on August 03, 2016, 04:44:42 pm
I'll be more than happy to help you answer this question and welcome to atarnotes!
Hi, the question is:
A three-digit number is selected from the numbers 3,4,5,7,8,9 with no repetition
What is the probability that he number formed is greater than 800?
Okay lets get started with this! I'll do it from the start just for clarifications sake :D
We know that anything that starts with a 3,4,5 or 7 will not be bigger than 800. So we can put them aside for now.
834, 835, 837, 839 etc. There are 4 different ways to fill in the third digit.
So for 83? there are 4 possibilities. There are 5 possibilities for 800's (eg 830,840,850)
Thus there are 20 possibilities it can start with an 8. This means that there are also 20 possibilities it can start with a 9. This makes 40 possibilities of it being greater than 800.
But how many possibilities are there? Well there are 20 each for 3, 4, 5, and 7 as well (total 80 possible numbers).
This makes 120 possible numbers. 40 of these are above 800.
Therefore, the possibility is 40/120 or 1/3 (simplifying the fraction).
If I have gone to fast or too slow please tell me so I can adjust my pace. I am currently at the top of my Gen Maths course but am unsure what level you are at. So I just assumed you would want the whole working out.
The short way is 6 x 5 x 4 = 120. (6 ways to fill the 1st number, 5 ways to fill the 2nd number and 4 ways to fill the 3rd number as they are without repetition).
Hope I helped and let me know what method you prefer!
Post by: roshanajabbour on August 03, 2016, 04:57:48 pm
Post by: studybuddy7777 on August 03, 2016, 05:02:20 pm
Thank you both! Helped a lot :)
No worries! Feel free to ask any more questions (or any other guests who would like to join/members who would like to post) if you are unsure about how to tackle any question!
My HSC Trial for Gen Maths is tomorrow so i wouldve thought this thread would be a bit more active lol
Post by: stephanieazzopardi on August 03, 2016, 05:02:57 pm
Hi, the question is:
A three-digit number is selected from the numbers 3,4,5,7,8,9 with no repetition.
What is the probability that he number formed is greater than 800?
I've already figured out the first part of the answer and found that the total numbers formed was 6P3=120
Can i please get help with finding the rest?
Just thought I'd post another way of explaining! The best thing to do in this example is to draw a set of boxes and in each box you place the number of possible outcomes at each stage. There will be three boxes in this solution because there are three numbers to be chosen.
| | x | | x | |
In each box, place the number of items that can be chosen from at each stage.
| 2 | x | 5 | x | 4 |
Explanation:
Box 1 = 2 because there are 2 possible numbers that can take the place of the first digit in this three digit number. Either 8 or 9 because the number has to be over 800.
Box 2 = 5 because there are 5 possible numbers that can take the place of the second digit in this three digit number. Either 8 or 9 has already been chosen, leaving 5 numbers left that can be chosen.
Box 3 = 4 because there 5 possible numbers that can take the place of the third digit in this three digit number. Because there is to be no repetition in our selection, the 8 or 9 + 1 other digit has already been taken, leaving 4 numbers left than can be chosen
| 2 | x | 5 | x | 4 | = 40 numbers will be over 800
Therefore, the probability that the number formed will be more than 800 is 40/120 = ⅓. (from provided first answer)
Post by: RuiAce on August 03, 2016, 05:53:25 pm
Post by: studybuddy7777 on August 03, 2016, 06:00:44 pm
Actually I would've written 2x5x4 as well but cause OP used permutation I decided go with the flow
Just a gentle reminder this is a general maths thread rui :)
But permutations=arrangements yes? Can't say im familiar with the word
Also your formula is really confusing, but looks awesome. Would you mind explaining it? Certainly no offence intended, just need to explain this a bit more to general students ;)
Post by: RuiAce on August 03, 2016, 06:53:09 pm
Just a gentle reminder this is a general maths thread rui :)Hm? Well
But permutations=arrangements yes? Can't say im familiar with the word
Also your formula is really confusing, but looks awesome. Would you mind explaining it? Certainly no offence intended, just need to explain this a bit more to general students ;)
First number: Two possible numbers to use.
Second number: Five possible numbers to use (because the sixth one is already used)
Third number: Four possible numbers to use (because the fifth one is also already used)
So 2 times 4 times 5
I find it easier to analyse each digit by itself, rather than use permutations.
P.S. Didn't Stephanie already explain it?
Post by: studybuddy7777 on August 03, 2016, 07:15:06 pm
Hm? Well
First number: Two possible numbers to use.
Second number: Five possible numbers to use (because the sixth one is already used)
Third number: Four possible numbers to use (because the fifth one is also already used)
So 2 times 4 times 5
I find it easier to analyse each digit by itself, rather than use permutations.
P.S. Didn't Stephanie already explain it?
Ahh ok thanks for that!
P.S. Did Stephanie already explain it? Im not sure but it didnt click with me last time..
Cheers :)
Post by: Stefan K on October 06, 2016, 11:20:53 pm
Post by: Stefan K on October 07, 2016, 12:05:11 am
Post by: jamonwindeyer on October 07, 2016, 12:13:19 am
Hi guys, not sure if they taught you this but my textbook never showed us this (at least I don't think so ??? ) and there are questions relation to it so here you go :)
Thanks Stefan! Just remember you won't have to remember anything for the exam that isn't on your formula/reference sheet! ;D
Post by: RuiAce on October 07, 2016, 12:20:06 am
Guys, I was wondering how to find the mean and sd using a calculator. I completely forgot :(Missed this one. This depends on what calculator you have.
Post by: Stefan K on October 08, 2016, 10:25:38 pm
Post by: roshanajabbour on October 11, 2016, 07:01:02 pm
Which expression could be used to find a value for the probability that it will rain on two
consecutive days in October in Mathsville?
(A) 8/31× 7/30
(B) 8/31 x 7/31
(C) 8/31 x 8/30
(D) 8/31 x 8/31
Post by: jakesilove on October 11, 2016, 07:11:51 pm
16 In Mathsville, there are on average eight rainy days in October.
Which expression could be used to find a value for the probability that it will rain on two
consecutive days in October in Mathsville?
(A) 8/31× 7/30
(B) 8/31 x 7/31
(C) 8/31 x 8/30
(D) 8/31 x 8/31
Hey! If there are 8 rainy days in 31 days on average, then all we can say for sure is that the probability of it raining on any given day is 8/31. Therefore, to rain on two consecutive days, the probability will be the likelihood of raining on the first day, times the probability of raining on the second day. So, the answer is (8/31)*(8/31) which is D!
Post by: roshanajabbour on October 11, 2016, 07:20:02 pm
Hey! If there are 8 rainy days in 31 days on average, then all we can say for sure is that the probability of it raining on any given day is 8/31. Therefore, to rain on two consecutive days, the probability will be the likelihood of raining on the first day, times the probability of raining on the second day. So, the answer is (8/31)*(8/31) which is D!Cheers! I think i may have mixed myself up with another type of question whilst determining this.
Post by: pughg16 on October 19, 2016, 04:48:11 pm
Cheers! I think i may have mixed myself up with another type of question whilst determining this.Don't worry, I made the same mistake when I was answering this question! I did 8/31 * 7/30, but my maths teacher told me how to do it!!