[Guest]

Dave loved to play the Lotto 6/49. One day while he was at his Grandfather's house, his Grandfather said to him, "Dave - you're a fool! I bet you'd have better odds of hitting an ant with a pin in a football field that winning that stupid lottery!". Dave replied, "That's impossible!" to which the Grandfather replies "So is your stupid lottery!". Now this got Dave mad, and he was always up for a challenge, and he set out to prove his grandfather wrong.

Who was right?

Assume that the ant is 1cm x 0.5cm and that Dave lives in Canada (for the football field size).

How big would the ant have to be to make the odds equal?

[Guest]

Does 6/49 mean he has to hit 6 numbers ranging from 1-49 and each number can only be drawn once?

[Guest]

Does 6/49 mean he has to hit 6 numbers ranging from 1-49 and each number can only be drawn once?

Yes

[Guest]

One question: How big are football fields in Canada?

(I'm American)

[Guest]

One question: How big are football fields in Canada?

(I'm American)

Just a bit bigger - although i have no idea why they are different. If anyone knows it would be interesting...

I didn't include the end zones:

Canadian Football Field

[Guest]

I found it to be 110 yards + (2) 20 yard endzones and 65 yards wide Comes out to be about 81,525,410 cm2.

[Guest]

assumed that: winning equals winning the jackpot

then probability of Dave winning the jackpot: 1/83,902,895 (49 C 6)

size of football field : 360 * 160 * 144 * 2.54 * 2.54 = 53,512,151.04 sq. cm.

probability of hitting an area of 0.5 sq.cm = 0.5/53,512,151.04 = 1/107,024,302.08

let the are to be hit = x sq.cm such that x/53,512,151.04 = 1/83,902,895

x = 1.5625 sq cm

if the ant were 1.25 cm * 1.25 or if it were 3.125 cm by 0.5 cm then the probabilities, hence the odds, would be equal

[Guest]

assumed that: winning equals winning the jackpot

then probability of Dave winning the jackpot: 1/83,902,895 (49 C 6)

size of football field : 360 * 160 * 144 * 2.54 * 2.54 = 53,512,151.04 sq. cm.

probability of hitting an area of 0.5 sq.cm = 0.5/53,512,151.04 = 1/107,024,302.08

let the are to be hit = x sq.cm such that x/53,512,151.04 = 1/83,902,895

x = 1.5625 sq cm

if the ant were 1.25 cm * 1.25 or if it were 3.125 cm by 0.5 cm then the probabilities, hence the odds, would be equal

right thinking, wrong odds on the lotto.

please use spoilers for your answers

[Guest]

then probability of Dave winning the jackpot: 1/83,902,895 (49 C 6)

Your reasoning seems correct, but not entirely sure where you're getting that math. C(49, 6) would be 13,983,816. Also 65 * 3 is 195 not 160.

Also, you may want to make use of the spoiler feature.

Probability of getting a perfect match on the lotto draw would be 1 in C(49, 6) which is 1 in 13,983,816.

Given the football field from the picture with 110x65yd dimensions, and assuming 1yd = 3ft = 36in = 91.44cm, total area of the field is

(110 x 91.44)x(65 x 91.44) = 59,783,106.24cm²

The ant is 1 x 0.5 cm = 0.5cm² and so hitting it would be the same as hitting any given 0.5cm² area which would be

0.5/59,783,106.24 = 1 in 119,566,212.5 chance.

It would appear that Dave is right - the chances of winning the lotto are better than hitting the ant.

In order for the ant's chances (of death) to be the same as the lotto, the ant would have to be 119,566,212,5 / 13,983,816 = 8.55 times larger. Using the same ratio of dimensions as the original ant, it would be about 2.92cm x 1.46cm.

Edited July 16, 2010 by jb_riddler

[Molly Mae]

Incidentally, they would both be wrong.

...they're Canadian. =P

The odds I came up with are 1 in 13,983,816 for the lottery.

So the ant would have to be about 3.862 sq cm

[Guest]

Well.. it says to hit "an ant", not a particular ant. So I think this would really depend on location, climate and many other variables. I mean, when was the last time you saw just one ant? If there are 2 million ants in the field, and they all happen to be above ground, that would change things significantly. But if it is arctic conditions, there may be zero ants... thus impossible to hit one unless you import..

Also, how big is this pin we are throwing? Do glancing blows count? Can the ant have the wherewithal to look up and attempt to evade?

Edited July 16, 2010 by mabus

[Guest]

Incidentally, they would both be wrong.

...they're Canadian. =P

The odds I came up with are 1 in 13,983,816 for the lottery.

So the ant would have to be about 3.862 sq cm

Hey - easy on us Canadians Eh .

Edited July 16, 2010 by littlej

[Guest]

Well.. it says to hit "an ant", not a particular ant. So I think this would really depend on location, climate and many other variables. I mean, when was the last time you saw just one ant? If there are 2 million ants in the field, and they all happen to be above ground, that would change things significantly. But if it is arctic conditions, there may be zero ants... thus impossible to hit one unless you import..

Also, how big is this pin we are throwing? Do glancing blows count? Can the ant have the wherewithal to look up and attempt to evade?

Awesome! All excellent points.

[Molly Mae]

I have assumed the below

The pin represents a single point.

The ant is one specific ant.

Th eant does not move.

The pin may strike one and only one location (no bouncing).

[Guest]

(64,350 sq ft * 144 * 2.54^2) / 13,993,816 = 4.28 sq cm

Your reasoning seems correct, but not entirely sure where you're getting that math. C(49, 6) would be 13,983,816. Also 65 * 3 is 195 not 160.

Also, you may want to make use of the spoiler feature.

Probability of getting a perfect match on the lotto draw would be 1 in C(49, 6) which is 1 in 13,983,816.

Given the football field from the picture with 110x65yd dimensions, and assuming 1yd = 3ft = 36in = 91.44cm, total area of the field is

(110 x 91.44)x(65 x 91.44) = 59,783,106.24cm²

The ant is 1 x 0.5 cm = 0.5cm² and so hitting it would be the same as hitting any given 0.5cm² area which would be

0.5/59,783,106.24 = 1 in 119,566,212.5 chance.

It would appear that Dave is right - the chances of winning the lotto are better than hitting the ant.

In order for the ant's chances (of death) to be the same as the lotto, the ant would have to be 119,566,212,5 / 13,983,816 = 8.55 times larger. Using the same ratio of dimensions as the original ant, it would be about 2.92cm x 1.46cm.

[Guest]

Dave loved to play the Lotto 6/49. One day while he was at his Grandfather's house, his Grandfather said to him, "Dave - you're a fool! I bet you'd have better odds of hitting an ant with a pin in a football field that winning that stupid lottery!". Dave replied, "That's impossible!" to which the Grandfather replies "So is your stupid lottery!". Now this got Dave mad, and he was always up for a challenge, and he set out to prove his grandfather wrong.

Who was right?

Assume that the ant is 1cm x 0.5cm and that Dave lives in Canada (for the football field size).

How big would the ant have to be to make the odds equal?

I'm sorry, but I don't see how this is possible to solve. It depends on how good Steve is with shooting pins at ants on football fields. For instance, if you played basketball against Michael Jordan, it wouldn't be half a chance you would win, half a chance he would win. And how many ants are on football field? Do football fields use insecticides?

[Guest]

Wait if its canada then is said football Soccer?

[Guest]

He could find an ant, walk up to it and hit it

You never specified throwing it