Math Problems!........share It Here!

[boy男孩]

Show the mathematical solution showing a person's chance to winnning a 6/42, 6/45 & 6/49 lotto.

 

How about 2, 3 or 4 persons winning the same draw?

[floppydrive]

6/42 lotto:

 

For n person(s), the chances of getting the 6 numbers are:

n * 42*41*40*39*38*37 = n*42!/36!

 

so for 1 person it's 42!/36!, for 2 people, it's 2*42!/36!, etc.

 

6/45 lotto:

 

For n person(s), the chances of getting the 6 numbers are:

n * 45*44*43*42*41*40 = n*45!/39!

 

6/49 lotto:

 

For n person(s), the chances of getting the 6 numbers are:

n * 49*48*47*46*45*44 = n*49!/43!

 

For lotto 6/X, where X is the number of numbers to choose from, and n is the number of winners for the same draw, the general equation is:

 

 

n * X!/(X-6)!

[boy男孩]

6/42 lotto:

 

For n person(s), the chances of getting the 6 numbers are:

n * 42*41*40*39*38*37 = n*42!/36!

 

so for 1 person it's 42!/36!, for 2 people, it's 2*42!/36!, etc.

 

6/45 lotto:

 

For n person(s), the chances of getting the 6 numbers are:

n * 45*44*43*42*41*40 = n*45!/39!

 

6/49 lotto:

 

For n person(s), the chances of getting the 6 numbers are:

n * 49*48*47*46*45*44 = n*49!/43!

 

For lotto 6/X, where X is the number of numbers to choose from, and n is the number of winners for the same draw, the general equation is:

 

 

n * X!/(X-6)!

hmmn. i believe something is wrong with your equations. for 1 thing, the chance or probabity of one person in winning a lottery decreases as the numbers of winners increases. wat u think?

[floppydrive]

I thought the question was what is the probability of 2 people winning the lotto on the same draw. If my understanding is correct, the chances for 2 people winning at the same time becomes slimmer than for one person winning it.

 

one person has a one in 42!/36! chance of winning the draw.

 

two people winning at the same time is one chance in 2*42!/36! to occur.

 

If we examine the probability of one person winning, the equation is still 42!/36!, regardless of the number of people entering the lotto. I would assume that a person's chance of winning is the same. He would receive a smaller sum, but his chances are still the same.

 

What do you think, Sir Boy?

 

Off topic, your picture looks very familiar... Are you from Jakarta?

[floppydrive]

I thought the question was what is the probability of 2 people winning the lotto on the same draw. If my understanding is correct, the chances for 2 people winning at the same time becomes slimmer than for one person winning it.

 

one person has a one in 42!/36! chance of winning the draw.

 

two people winning at the same time is one chance in 2*42!/36! to occur.

 

The above is from the perspective of the lotto organizer, checking what are the chance of having multiple winners.

 

Let's now take it from the perspective of the chances of ONE person winning.

 

For him or her to win, he or she has to choose the correct 6 numbers out of 42. It doesn't matter how many people enter, becuase what matters is for the entrant to get all 6 numbers correct.

 

If we examine the probability of one person winning, the equation is still 42!/36!, regardless of the number of people entering the lotto. I would assume that a person's chance of winning is the same. He would receive a smaller sum, but his chances are still the same.

 

What do you think, Sir Boy?

 

Off topic, your picture looks very familiar... Are you from Jakarta?

[boy男孩]

I thought the question was what is the probability of 2 people winning the lotto on the same draw. If my understanding is correct, the chances for 2 people winning at the same time becomes slimmer than for one person winning it.

 

one person has a one in 42!/36! chance of winning the draw.

 

two people winning at the same time is one chance in 2*42!/36! to occur.

 

The above is from the perspective of the lotto organizer, checking what are the chance of having multiple winners.

 

Let's now take it from the perspective of the chances of ONE person winning.

 

For him or her to win, he or she has to choose the correct 6 numbers out of 42. It doesn't matter how many people enter, becuase what matters is for the entrant to get all 6 numbers correct.

 

If we examine the probability of one person winning, the equation is still 42!/36!, regardless of the number of people entering the lotto. I would assume that a person's chance of winning is the same. He would receive a smaller sum, but his chances are still the same.

 

What do you think, Sir Boy?

 

Off topic, your picture looks very familiar... Are you from Jakarta?

oh yes, you are right I think we share the same view that the chance of any person to win a lotto draw is the same assuming everybody has the same number of bets. It is also true that the chance of a single winner in a draw is higher than the chance of multiple winners. But your eqn says otherwise, the more winner the bigger the chance. I think it should be the reciprocal.

 

1

------------- or 6! where n = the number of winners

n* 42! ----------

------- n*42!

6!

 

but on the other hand, according to some experts the one's chance to win a 6/42 lotto draw is 1 is to 5.3 million, because there are approximately 5.3 million possible combinations for the 6/42 lotto. this means you need at least 53million pesos to bet for you to be a sure winner. Now, I can not derived these figures from your eqns. Any more thoughts?

 

(off the record, oh yes i'm from jakarta )

[boy男孩]

oh yes, you are right I think we share the same view that the chance of any person to win a lotto draw is the same assuming everybody has the same number of bets. It is also true that the chance of a single winner in a draw is higher than the chance of multiple winners. But your eqn says otherwise, the more winner the bigger the chance. I think it should be the reciprocal.

 

1

------------- or 6! where n = the number of winners

n* 42! ----------

------- n*42!

6!

 

but on the other hand, according to some experts the one's chance to win a 6/42 lotto draw is 1 is to 5.3 million, because there are approximately 5.3 million possible combinations for the 6/42 lotto. this means you need at least 53million pesos to bet for you to be a sure winner. Now, I can not derived these figures from your eqns. Any more thoughts?

 

(off the record, oh yes i'm from jakarta )

Sorry for the mess! What you see is not what you get. This is the edited post.

 

 

oh yes, you are right I think we share the same view that the chance of any person to win a lotto draw is the same assuming everybody has the same number of bets. It is also true that the chance of a single winner in a draw is higher than the chance of multiple winners. But your eqn says otherwise, the more winner the bigger the chance. I think it should be the reciprocal.

 

1

-------------

n* 42!

-------

6!

 

or

 

6!

---------

n*42!

 

 

where n = the number of winners

 

 

 

but on the other hand, according to some experts the one's chance to win a 6/42 lotto draw is 1 is to 5.3 million, because there are approximately 5.3 million possible combinations for the 6/42 lotto. this means you need at least 53million pesos to bet for you to be a sure winner. Now, I can not derived these figures from your eqns. Any more thoughts?

 

(off the record, oh yes i'm from jakarta )

[floppydrive]

It is also true that the chance of a single winner in a draw is higher than the chance of multiple winners. But your eqn says otherwise, the more winner the bigger the chance.

I think the numbers are getting confusing. I think it's just a matter of interpretation like specific gravity and density - it means the same relationship but read in different ways.

 

The chances for one winner is higher than for multiple winners - this we agree.

 

But it can be seen from the equations I wrote that this is so:

 

For one winner he has a 1 in 5.3 million chance.

 

For two winners, there is a 1 in 10.6 million chance. So the there really is a slimmer chance of having multiple winners.

 

The numbers are growing but it is in the interpretation that we differed.

 

This is the same as your equation which is the reciprocal.

[boy男孩]

I think the numbers are getting confusing. I think it's just a matter of interpretation like specific gravity and density - it means the same relationship but read in different ways.

 

The chances for one winner is higher than for multiple winners - this we agree.

 

But it can be seen from the equations I wrote that this is so:

 

For one winner he has a 1 in 5.3 million chance.

 

For two winners, there is a 1 in 10.6 million chance. So the there really is a slimmer chance of having multiple winners.

 

The numbers are growing but it is in the interpretation that we differed.

 

This is the same as your equation which is the reciprocal.

okey. but then again, the eqn 42!/36! = 3,776,965,920. i believe you missed out something.

[floppydrive]

okey. but then again, the eqn 42!/36! = 3,776,965,920. i believe you missed out something.

Oops, I did miss something.

 

42!/36! gives all the unique combinations of the 6 numbers out of 42, but the numbers have to be picked at the exact order.

 

Since lotto allows us the combination of the 6 numbers in any order, we have to divide it by the number of possible combinations of the 6 numbers.

 

So it should be:

 

42!/36!

-------- = 5,245,786

6!

 

or 1 chance in 5,245,786

 

since we are after the inverse,

 

6!

-------- = 0.000,000,190,629

42!/36!

 

or 0.0000190629 % probability

or 0.190629ppm

 

Sheesh - in a production system, that's close to impossible!

 

So it must be true - winning the lotto is an act of GOD ...

[x8...]

alphabets antone? (commercial lng)

 

 

how many letters are there in the english alphabet?

 

26?

 

times have changed....

 

24 lang.

 

what 2 letters were kicked out ot the alphabet?

[boy男孩]

Oops, I did miss something.

 

42!/36! gives all the unique combinations of the 6 numbers out of 42, but the numbers have to be picked at the exact order.

 

Since lotto allows us the combination of the 6 numbers in any order, we have to divide it by the number of possible combinations of the 6 numbers.

 

So it should be:

 

42!/36!

-------- = 5,245,786

6!

 

or 1 chance in 5,245,786

 

since we are after the inverse,

 

6!

-------- = 0.000,000,190,629

42!/36!

 

or 0.0000190629 % probability

or 0.190629ppm

 

Sheesh - in a production system, that's close to impossible!

 

So it must be true - winning the lotto is an act of GOD ...

Ok doki. so, For philippine lotto draws. the probability of winnning is

 

 

(L-6)! 6! / W*L! where W is no. of winners, L = lotto game i.e. 42, 45 & 49.

[Ekans]

any number divided by 0

 

sino may alam nito

[floppydrive]

any number divided by 0

 

sino may alam nito

Pag sa calculator o computer, and sagot ay "ERROR".

 

Pero kung pag-aaralan, ang sagot dapat ay INFINITY, except kung Zero yung ididivide.

 

Kung Zero yung ididivide, zero and sagot.

[quintix]

on dividing by zero:

 

to divide by a number x is to multiply by its multiplicative inverse, 1/x

 

the reciprocal/inverse of a number is that which when multiplied by the number is 1

 

so we need the value of 1/x when x=0. however, any number multiplied by zero is zero (zero property of multiplication).

 

and so zero has no inverse, and we can't divide anything by it. ganun na yun, parang langis at tubig na di maghahalo kahit ano pa ang bate mo.

 

 

---------------------------

 

regarding the lotto, let us simplify the game first. hulaan ng labas sa six-sided die, tapos tatlo lang tao sa mundo na tag-isa ang mga hula. kumbaga 1-6 ang laro.

 

chances of winning? 1/6, for each player

 

chances of no person winning: (5/6)(5/6)(5/6) = 125/216

chances of exactly 1 person winning: 3(1/6)(5/6)(5/6) = 75/216

chances of exactly 2 persons winning: 3(1/6)(1/6)(5/6) = 15/216

chances of all persons winning: (1/6)(1/6)(1/6) = 1/216

total probability: 1 (125+75+15+1=216)

 

the point of it all: least likely scenario is that everyone wins, least likely is no one wins, with other possiblities falling inbetween. pero di masasagot yang lotto question kung walang assumption kung ilan ang tumaya, kung ilang numero ang tinaya ng mga tao, kung nandadaya ba yung mga taga-PCSO, etc.

 

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i move that this thread be closed!