Suppose 20 people each pay $10 into a fund to buy chances for this week\'s lotte

Question

Suppose 20 people each pay $10 into a fund to buy chances for this week's lottery. They will collect $200 and thus buy 200 tickets. If any of the 200 tickets is a winner, the prize money will be shared equally by all 20 participants. One of the participants was wondering if buying more tickets actually decreased the chances of each ticket because it increases the number of tickets in the ticket pool.

Answer the following questions:

-Does buying more tickets increase or decrease your chances of winning?
-Does your answer change if instead of a lottery, the tickets are for a raffle, and the winner is selected only from the tickets purchased?

Explanation / Answer

Buying more tickets increase the chance of winning, as probability of winning number getting increases.

Probability of winning = (200+ additional number of tickets bought) / total number of tickets

Which is greater than

probability of winning = (200/ total number of tickets )

Yes , if instead of lottery the tickets are for a raffle, buying more tickets decreases the chance of winning

Probability of winning = number of tickets bought/ total number of tickets sold

As with increase in number of tickets bought, number of tickets sold also increases

It may decrease the chance of winning

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