How to Calculate Lottery Odds for 6/49 or Powerball

My recent Decoded Science article, “Winning Powerball Tickets in Arizona and Missouri: How to Calculate the (Slim) Odds“, takes aim at the wildly popular American powerball lottery.

How to Compute the Probability for  6/49 Compared to the American Powerball Lottery

"Taiwan Lottery Dream Sheet" by Prince Roy
“Taiwan Lottery Dream Sheet” by Prince Roy

The formula is actually the same for any lottery “without replacement and regardless of order“, and it’s already explained in my Decoded Science article.

The key difference comes from the number of balls in the urn, and how many are selected. To win the 6/49 jackpot requires selecting 6 numbers from the pool of 49. We need to calculate the number of combinations of 6 balls from 49:

  • The number of combinations = 49*48*47*46*45*44/(6!) = 49*48*47*46*45*44/(6*5*4*3*2*1) = 13,983,816.
  • Therefore the probability of winning the 6/49 jackpot is 1/13,983,816, by my calculations.

By comparison, the probability of winning the Powerball jackpot is 1 in 175,223,510. That’s about 12.5 times worse than the chance for winning 6/49.

Could We Compute the Odds of Winning Lotto Max or Other Canadian Lotteries?

Yes, of course we can compute the odds of winning any fair lottery “without replacement and regardless of order” using the same formula. We just need to learn the total number of balls in the pool, and how many are to be selected.

The Canada-wide Lotto Max jackpot requires selecting 7 numbers from a pool of 49, so the number of combinations is:

  • 49*48*47*46*45*44*43/(7!) = 49*48*47*46*45*44*43/(7*6*5*4*3*2*1) = 85,900,584 by my calculation.
  • Therefore Lotto Max has 85,900,584/13,983,816 = 6.14 times as many combinations as does the 6/49 lottery.

Publicity for my Articles about Calculating the Odds of Winning a Lottery

As always my Blog of Writing provides publicity, where “Preview of Calculating Powerball Odds” offers a high-probability writing tip.

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Thank you for reading about the probability of winning Lotto 4/49 or the American Powerball lottery.

Disclaimer: The information contained in this article is for educational purposes only and should not be used to encourage gambling or gaming activities; certainly not to the point where it interferes with normal household finances.

Does Toronto Stand Alone in Banning Plastic Bags?

Does Toronto stand alone with its ban on disposable plastic bags for shopping?

No, Toronto is in good company, according to a well-researched infographic from who asked me to publish it. (Updated Oct. 11, 2015): the infographic is no longer available online.

(Updated Nov. 28, 2012): Toronto City Council voted 38-7 this morning, Nov. 28 2012, to postpone the ban on disposable plastic shopping bags. The current plan is to “revisit the discussion on the ban in June (2013) following public consultation”.  For the moment, Toronto neither stands alone nor does it ban plastic bags.

Problems and Solutions for Disposable Plastic Bags

"Plastic Bag Nightmare" image by Zainub (Zainub Razvi)
“Plastic Bag Nightmare” image by Zainub (Zainub Razvi)

Major cities such as Washington DC imposed a shopping bag fee; others have banned their use altogether. Other Canadian cities might follow suit, if their provincial legislation gives them the appropriate authority. (Apparently this won’t happen in BC without those changes, for example).

The problem is that the developed world, including Toronto, uses and throws away a huge number of plastic bags every day, week and year. The total amount clogs landfills and pollutes the oceans. We recycle very little of this plastic, but require petroleum as the feedstock to make new plastic bags. Although we don’t often think that disposable plastic bags cause pollution, they do kill animals that try to eat them, and make it more difficult for plants to grow.

There is a limit to how often one can reuse a plastic shopping bag; eventually it gets a rip or tear. Recycling plastic bags could be one answer, but we haven’t demonstrated much success.

It’s easy to protect our environment by buying multi-use or reusable plastic bags; they are strong and sturdy, having served our household well for several years. It’s easy to buy reusable plastic shopping bags in many stores in Toronto.

Toronto’s ban on plastic bags is a current controversy; see  “Plastics group suing city over bag ban” (by David Rider of the Toronto Star on Nov. 20, 2012) with its own back links.

I don’t normally comment on political issues; but although this infographic’s focus is largely on the USA, it makes an important environmental point. I’d like to consider this article  about the plastic bag ban in Toronto as a public service announcement.

LearnStuff‘s original article is also gone.

(Updated Feb. 22, 2013): Read about a related topic in “What is Climate Change Doing to the Earth, per LearnStuff“, with their latest infographic.

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DeHaan Services writes web site or advertising copy for clients. Our skills are demonstrated in online articles in Decoded Science, as well as other web sites. That’s why we highlight these online articles on this blog page.

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Thank you for reading this article and infographic about banning plastic bags in Toronto.

Three Outdoor Carol Events in Dec. 2012 in Eastern Toronto

Choose one or more nearly-free outdoor Christmas caroling events in eastern Toronto in early December 2012.

(Updated Nov. 24, 2014): Or “Enjoy Christmas Carols Outdoors in Toronto for 2014“. (Updated Nov. 30, 2013): I found some new and some returning events: see “2013 Outdoor Christmas Caroling in Toronto and Mississauga“.

Singing Christmas carols is a terrific family activity during the Yule season. These three events also answer the question, “Where can my kids see Santa Claus other than in a shopping mall in Toronto”?

Where to go Christmas Caroling in Toronto?

"Outdoor Carolling at Night" image by The Wu's Photo Land
“Outdoor Carolling at Night” image by The Wu’s Photo Land

I easily found three answers to the question, “Where to go Christmas caroling in Toronto?”: Kew Gardens, Sunnybrook Park or Glen Stewart Park.

The secret is to know both “when” and “exactly where“.

Christmas Carols in Kew Gardens in Toronto

On Saturday Dec. 1st, 2012, head for the Alex Christie Bandshell in Kew Gardens. If you arrive by 5pm, you will see the lighting of the Christmas Tree as well as a visit by Mr. and Mrs. Santa Claus. Sing Christmas carols along with the rest of the crowd.

This is a nearly-free event, but the Beaches Lions’ Club appreciates donations of “Loonies for the Lions”.

The festivities end by 7pm, so this is a very family-friendly event. Actually, all Christmas festivals befriend children as well as adults.

Kew Gardens is on Queen St. East, roughly midway between Woodbine Ave. and Main Street. It’s best to take TTC; either the 501 Queen Streetcar or a bus south from the Woodbine or Main stations on the Bloor-Danforth line.

My one concern for your family is that this event covers suppertime, but I’m sure that Toronto’s restaurants in the Beach neighbourhood would welcome you that evening.

Christmas Carols in the Pines by Brentcliffe Road

The Northlea United Church at 125 Brentcliffe Road will host a one-hour session of Christmas carolling on Sunday Dec. 9, 2012 from 7 to 8pm. The Salvation Army will provide the band, but participants should bring their own flashlights.

Here is my direction for drivers from the far east of Toronto. Drive west along Eglinton, from Don Mills and past Leslie. Eventually the next right turn is north onto Brentcliffe which curves west and north as it goes past the church.Brentcliffe eventually connects to Glenvale Blvd.; turn left and drive west to connect to Bayview Ave.

The park is on the north border of the church. Santa Claus has asked a Boy Scout troop to provide hot chocolate. There’s no word about making donations, but I’d be prepared to help the Salvation Army with some coins, since it is the Yuletide season.

Caroling in Glen Stewart Park

Head back to the Upper Eastern Beach on Tuesday Dec. 11, 2012 and sing carols in Glen Stewart Park from 7:30pm for an hour.

Once again the Salvation Army, a local United Church, Boy Scouts and Santa Claus join forces to sing sweetly in a Toronto park.

Glen Stewart Park is south of Kingston Road, between Glen Manor Drive and Beech Ave. but extends south to touch Queen St. East. I’d start from Queen Street and head north, since the venue is “south of the bridge”.

This is definitely a nearly-free event, as the Salvation Army will receive a collection.

My Thought about Christmas Caroling

I can’t imagine a Christmas without singing carols, largely because my church always ensures we have ample opportunity. Those of you who attend a church regularly, or just during the Advent season, might enjoy the extra atmosphere from singing outdoors.

For those who don’t follow the Christian faith, it’s still an enjoyable passtime to sing Yuletide songs. Some Christians bemoan “Xmas presents”, the frantic rush to buy Christmas presents, and the way the visit by Santa Claus with his reindeer has supplanted the birth of Jesus in popular culture. Nonetheless, many cultures celebrate the winter solstice; if you’re from a different faith or culture, you might consider this to be an educational opportunity to meet some neighbours.

Besides, I recently wrote “Must Toronto Ask When is Diwali in 2012?” and, last year, “A Quick Introduction to Kwanzaa Holiday Entertaining“. If you have more suggestions on religious festivals celebrated in Toronto during the winter, please let me know.

Reference (added Nov. 26, 2012): Beach Metro News, Nov. 20, 2012 print edition, Community Events notices page.

(Updated Dec. 9, 2012): Check Roots Canada‘s outdoor wear for women or men to prepare for any outdoor winter activities in Toronto. At the time of writing, the women’s Tremblant Down Sweater is 30% off; so is the men’s Delirium Insulator Jacket.

As a possible follow-up to Christmas caroling, you might search for “Christmas books for children” at Barnes and Noble or at Chapters Indigo. “The Night before Christmas” and “How the Grinch Stole Christmas” are classics.

Looking for More Annual Toronto Events?

Check the “annual events” or “Toronto events” categories toward the end of the left-hand menu for other fascinating, free or frugal annual events in Toronto.

Disclaimer: DeHaan Services has no relationship to the organizer(s); I am not reimbursed for writing this article. However, DeHaan Services does write web site or advertising copy for clients. Our skills are demonstrated in online articles in Decoded Science and other online sites. That’s why DeHaan Services highlight these online articles on this blog page.

Writing for Clients; Annual Events in Toronto and the GTA