a batch of 350 raffle tickets contains four winning tickets. you buy four tickets. what is the probability that you have at least one winning ticket?
To calculate the probability of at least one winning ticket, we can use the concept of complementary probability.
The probability of not winning with a single ticket is given by (350 - 4) / 350, as there are 350 tickets in total and 4 of them are winning tickets.
The probability of not winning with all four tickets can be calculated by taking the probability of not winning with a single ticket and multiplying it four times:
[(350 - 4) / 350] * [(350 - 4) / 350] * [(350 - 4) / 350] * [(350 - 4) / 350]
To find the probability of winning at least once, we can subtract the probability of not winning with all four tickets from 1 (the total probability).
Therefore, the probability of winning at least once with four tickets is:
1 - [(350 - 4) / 350] * [(350 - 4) / 350] * [(350 - 4) / 350] * [(350 - 4) / 350]
To find the probability of having at least one winning ticket, we need to calculate the complement of having no winning tickets.
Let's break down the problem step by step:
Step 1: Calculate the probability of not winning with a single ticket.
Out of 350 tickets, there are 346 losing tickets and 4 winning tickets. So, the probability of not winning with a single ticket is 346/350.
Step 2: Calculate the probability of not winning with all four tickets.
Since the tickets are independent events, we multiply the probability of not winning with a single ticket by itself four times:
(346/350) * (346/350) * (346/350) * (346/350) = (346/350)^4.
Step 3: Calculate the complement of not winning with all four tickets.
Since we want to find the probability of having at least one winning ticket, we need to subtract the probability of not winning with all four tickets from 1. So, the complement is 1 - (346/350)^4.
Step 4: Calculate the probability of having at least one winning ticket.
After performing the calculation, the probability of having at least one winning ticket is approximately 0.0434 or 4.34%.
Therefore, the probability that you have at least one winning ticket is approximately 0.0434 or 4.34%.