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## More Chance of Being Trampled By a Herd of Elephants!

Probability puzzles require you to weigh all the possibilities and pick the most likely outcome.

 Puzzle ID: #37648 Fun: (2.24) Difficulty: (2.37) Category: Probability Submitted By: leftclick Corrected By: nerdyiscool

Leftclick Lotteries Inc. runs a lottery in which 5 balls are drawn from a barrel of numbered white balls (so that each white ball may be drawn once only), and 1 ball is drawn from a different barrel of numbered black balls. There are 45 white balls and 45 black balls. Players must correctly select the numbers of all 5 white balls, as well as that of the black ball in order to win the main prize.

What is the probability of winning the main prize with any single given entry?

The probability of winning the main prize is 1 in 54,979,155.

The probability of winning is the probability of guessing each ball correctly. For the black ball, this is 1/45. For each white ball, it is 5/45 (there are 5 correct balls out of 45 possible), 4/44 (there is 1 less correct ball and 1 less to choose from), 3/43, 2/42 and 1/41. This gives a probability of winning of 1 in 45*(45!)/(40!)*(5!), or 1 in 54,979,155.

The title is an expression that describes an event as being highly unlikely. Of course, the actual chance of being trampled by a herd of elephants is very difficult to measure and varies widely!

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