Lottery Luck In 1996, a New York couple won \$2.5 million in the state lottery. Eleven years later, the couple won \$5 million in the state lottery using the same set of numbers. The odds of winning the New York lottery twice are roughly 1 in 16 trillion, described by a lottery spokesperson as “galactically astronomical.” Although it is highly unlikely that an individual will win the lottery twice, it is not “galactically astronomical” that someone will win a lottery twice. Explain why this is the case.

Verified step by step guidance

1. Step 1: Understand the difference between the probability of a specific individual winning twice and the probability that someone, among many players, wins twice. The odds of 1 in 16 trillion refer to a particular person winning twice with the same numbers.
2. Step 2: Recognize that the lottery has millions of players, each with their own chance to win. When considering all players collectively, the chance that at least one person wins twice increases significantly.
3. Step 3: Use the concept of the 'multiple comparisons' or 'multiple trials' effect, which means that even very rare events become more likely when many independent trials or participants are involved.
4. Step 4: To quantify this, calculate the probability that no one wins twice by raising the probability of an individual not winning twice to the power of the number of players, then subtract this from 1 to find the probability that at least one person wins twice.
5. Step 5: Conclude that while the odds for a single individual are astronomically low, the large number of participants makes it not so surprising that someone eventually wins twice, explaining why the event is not 'galactically astronomical' overall.

Key Concepts

Probability of Independent Events

The probability of two independent events both occurring is the product of their individual probabilities. Winning the lottery twice involves multiplying the already tiny chance of winning once by itself, resulting in an extremely small probability for a specific individual.

Law of Large Numbers and Multiple Trials

When many people play the lottery over many draws, the chance that someone, not a specific person, wins twice increases. Large numbers of trials and participants make rare events more likely to occur somewhere in the population.

Misinterpretation of Probability in Real-World Contexts

People often confuse the improbability of a specific individual winning twice with the likelihood that some individual will win twice. The latter is more probable because it considers all players and all draws, not just one person's odds.