Posts Tagged ‘average probability’

Straight vs. Full House

Tuesday, August 14th, 2018

On another fine evening, there was a heated discussion at the Royal Flush Card Club as to how many occurrences of Full House and Straight would occur in the course of 30 throws of five poker dice.

Bing Jones III was betting $100 against Franz Fingerflitzer that he would get at least two instances of a Full House, the latter claiming at least two Straights during the trial – ties leading to a rematch until a winner emerged.

Lots of paper was expended and the whisky flowed freely while members of the Royal Flush Card Club busied themselves calculating the probabilities involved for throwing a Full House and a Straight.

However, accuracy and interest faded rapidly as whisky was poured, and this task was abandoned in favor of registering bets and proposing exuberant toasts, expectations rising to a high pitch, as if prior to a championship horse race.

Who do you think won the bet, Bing Jones III or Franz Fingerflitzer?

The Cereal Boxes

Sunday, November 13th, 2016

“Mommy, I want my cereal, my Munchy Crunchies,” pleaded Junior at the breakfast table. Mommy placed the cereal box, almond milk and honey in front of Junior.

While munching away Junior was avidly reading the promotional text on the back of the cereal box.

“Mommy, it says here that if I collect five famous Disney character cards, I will get a prize – a scout compass. There is one card in each box. Let’s quickly buy five boxes of Munchy Crunchies so I can get the compass for my Boy Scout trips,” suggested Junior with a bright enthusiastic look.

Daddy overheard Junior. “It doesn’t quite work that way, son. Maybe the five boxes we buy all have the same character card, or maybe just one different card.”

Junior was not discouraged. “It also says that cards have one of five colors on the other side: red, blue, green, yellow and orange,” informed Junior. “If all of the five character cards have a red back side, I can also win a Speedo bicycle. Please, daddy, we have to buy more boxes today,” pleaded Junior, munching away faster.

“Hmm,” said daddy.

“And, daddy, it also says that in one of every thousand boxes there is a gift card for a free trip to Disneyland for a family of three, with all expenses paid,” said Junior beaming.

Daddy became more interested. “Hmm, I will work out our chances for all this,” he said prudently, grabbed his calculator and went to his work room.

“Thanks, dad.” Junior was beaming with pleasure, thinking of the great prizes he would win and how much he would enjoy going to Disneyland.

Mommy cleaned the table. Then she made two cups of coffee and went to talk with daddy.

 

Can you help daddy work out how many cereal boxes on the average he will have to buy for Junior to obtain the five Disney characters and win a scout compass?

How many cereal boxes on average will win the red bicycle?

And how many boxes on average for a family trip to Disneyland?