A lottery game that is run in the United States is one in which players choose a three-digit number between 000 and 999. A player wins if his or her three-digit number is chosen. The physical mechanism that is used to draw the winning number gives each possibility an equal chance.

Every day, John buys a lottery ticket with the number 555 for the lottery described above. He has played 999 times and has never won. He reasons that since tomorrow will be his 1000th time and the probability of winning is 1/1000, he will have to win tomorrow. Explain whether or not John's reasoning is correct.

Question

A lottery game that is run in the United States is one in which players choose a three-digit number between 000 and 999. A player wins if his or her three-digit number is chosen. The physical mechanism that is used to draw the winning number gives each possibility an equal chance.

Every day, John buys a lottery ticket with the number 555 for the lottery described above. He has played 999 times and has never won. He reasons that since tomorrow will be his 1000th time and the probability of winning is 1/1000, he will have to win tomorrow. Explain whether or not John's reasoning is correct.

anonymous · Answer

The probability of each time he plays does not accumulate. Namely each time he plays, after it is over, his win or loss does not affect the next round because the next round he could have picked a different number. The only way he increases his chance of winning is to buy multiple tickets per round.