# probability

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A batch of 350 raffle tickets contatins 4 winning tickets. You buy 4 tickets. What is the probability that you have:

a.) No winning tickets?

b.) All winning tickets?

c.) At least one winning ticket?

d.) At least one non-winning ticket?

• probability - ,

there are 346 non-winning tickets in the batch.
So the prob of all 4 being non-winning is
(346/350)(345/349)(344/348)(343/347)
= .9549

or, if you know the C(n,r) combination topic,
it would be C(346,4)/C(350,4) = .9549

b) prob = (4/350)(3/349)(2/348)(1/347)
= .000000001
or C(4,4)/C(350,4) = .000000001

c) at least one winning ticket
= 1 - prob(all losing tickets)
= 1 - .9549 = .0451

d) at least one non-winner
= 1 - .000000001 = .999999999

• probability - ,

Sixteen batteries are tested to see if they last as long as manufacturers claim.Four batteries fail the test. Two are selected at random without replacement. Find the probability that both batteries fail the test. Find the probability that both batteries pass the test. Find the probability that at least one battery fails the test. Which of the events can be considered unusual? Explain