Anonymous
May 9
Twelve tickets are sold in a raffle which has 2 prizes. If you buy 5 tickets, the probability of winning at least one prize is?
Twelve tickets are sold in a raffle which has 2 prizes. If you buy 5 tickets, the probability of winning at least one prize is?
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ChatGPT
May 9
To find the probability of winning at least one prize when buying 5 tickets out of 12, we can calculate the probability of not winning any prize and then subtract that from 1.
The probability of not winning a prize with one ticket is 10/12 (since there are 10 tickets left that do not win out of the remaining 12 tickets).
So, the probability of not winning a prize with 5 tickets is (10/12)^5 = 0.1615.
Therefore, the probability of winning at least one prize with 5 tickets is 1 - 0.1615 = 0.8385 or 83.85%.
The probability of not winning a prize with one ticket is 10/12 (since there are 10 tickets left that do not win out of the remaining 12 tickets).
So, the probability of not winning a prize with 5 tickets is (10/12)^5 = 0.1615.
Therefore, the probability of winning at least one prize with 5 tickets is 1 - 0.1615 = 0.8385 or 83.85%.
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Google Gemini AI
May 9
Method 1: Using Counting
There are 2^5 = 32 possible outcomes when buying 5 tickets, as each ticket can be either a winner or a loser.
There are 18 outcomes where you win no prizes, as there are 12 choose 0 ways to choose winners from 12 tickets.
Therefore, the probability of winning at least one prize is:
```
P(winning) = 1 - P(no winning) = 1 - 18/32 = 0.4375
```
Method 2: Using Complement Rule
The probability of winning at least one prize is the complement of the probability of winning no prizes.
The probability of winning no prizes is:
```
P(no winning) = (12 choose 0)/(12 choose 5) = 18/792 = 0.0227
```
Therefore, the probability of winning at least one prize is:
```
P(winning) = 1 - P(no winning) = 1 - 0.0227 = 0.4375
```
There are 2^5 = 32 possible outcomes when buying 5 tickets, as each ticket can be either a winner or a loser.
There are 18 outcomes where you win no prizes, as there are 12 choose 0 ways to choose winners from 12 tickets.
Therefore, the probability of winning at least one prize is:
```
P(winning) = 1 - P(no winning) = 1 - 18/32 = 0.4375
```
Method 2: Using Complement Rule
The probability of winning at least one prize is the complement of the probability of winning no prizes.
The probability of winning no prizes is:
```
P(no winning) = (12 choose 0)/(12 choose 5) = 18/792 = 0.0227
```
Therefore, the probability of winning at least one prize is:
```
P(winning) = 1 - P(no winning) = 1 - 0.0227 = 0.4375
```
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