A batch of 350 raffle tickets contains 4 winning tickets. You buy 4 tickets. What is the probability you have no winning tickets?
b.) all winning tickets?
c.) at least 1 winning ticket?
d.) At least 1 non-winning ticket?
No winning? 346/350*345/349*344*348*343*347
There are four ways to get at least one winning ticket:
WLLL
WWLL
WWWL
WWWW
Pr(at least one winning ticket)=sum prob of all those.
To calculate the probabilities, we need to determine the total number of possible outcomes and the number of favorable outcomes for each scenario.
First, let's find the total number of possible outcomes. Since there are 350 tickets in the batch, the total number of possible outcomes is 350.
a.) Probability of having no winning tickets:
The number of favorable outcomes is the number of ways you can choose 4 non-winning tickets from the batch of 350. Since there are 346 non-winning tickets in the batch, the number of favorable outcomes is given by the combination formula C(346, 4) or 346! / (4! * (346-4)!). Thus, the probability is:
P(no winning tickets) = favorable outcomes / total outcomes
P(no winning tickets) = C(346, 4) / 350
b.) Probability of having all winning tickets:
In this case, the number of favorable outcomes is 4, as there are 4 winning tickets in the batch. So the probability is:
P(all winning tickets) = favorable outcomes / total outcomes
P(all winning tickets) = 4 / 350
c.) Probability of having at least 1 winning ticket:
To calculate this probability, we will use the concept of complementary probability. The complementary probability of having at least 1 winning ticket is the probability of having no winning tickets subtracted from 1. So the probability of having at least 1 winning ticket is:
P(at least 1 winning ticket) = 1 - P(no winning tickets)
d.) Probability of having at least 1 non-winning ticket:
We can use the same approach as in c) to calculate this probability. The complementary probability of having at least 1 non-winning ticket is the probability of having all winning tickets, which is 4/350.
P(at least 1 non-winning ticket) = 1 - P(all winning tickets)
Note: Remember to simplify the probabilities to their simplest form or convert them to decimal or percentage format if necessary.