(From ABC News, July 8, 2010). Maybe the odds of winning the lottery would be a

Question

(From ABC News, July 8, 2010). Maybe the odds of winning the lottery would be a lot better if Joan Ginther would stop buying all the good tickets.

You may have heard of the Las Vegas resident, whom you probably want sitting next to you when an asteroid, shot by aliens, is aimed at your planet. Joan recently cashed in a winning $10 million scratch-off ticket, making the lucky woman a four-time lottery winner.

1993: $5.4 million (paid in yearly installments). Probability: 1/15,800,000.

2006: $2 million (lump-sum payoff). Probability: 1/1,028,338.

2008: $3 million (lump-sum payoff). Probability: 1/909,000.

2010: $10 million (lump-sum payoff). Probability: 1/1,200,000 (end quote from ABC).

The probability of two or more independent events all happening is the product of their individual probabilities. Compare the probability of Joan winning all four lotteries with the probability of picking, at random, a grain of sand pained red that is hidden somewhere within the Sahara desert.

Explanation / Answer

Probability of Joan winning all four lotteries = (1/15,800,000)x(1/1,028,338)x(1/909,000)x(1/1,200,000)

=5.64x10-26

Assume that 1 gram of sand contains 100grains

Let us estimate that the total amount of sand in sahara desert is 1,000,000,000 tonnes

So, total number of grains =

1x109 x1000x1000

=1x1015

Probability of finding a sand grain painted red when you randomly pick a grain from Sahara desert = 1/1015

= 1x10-15

So, winning a lottery four times has lesser probability that finfing the grain of sand.

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