In the lottery there are 5 numbers rolled from 35 numbers and for 3 right quessed numbers there is a third price. What's the propability that we will win the third price if we buy one ticket with 5 numbers.
Probability of winning in the lottery
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probability
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1Hi, welcome to math.SE. Please clarify your question as question is not clear.Like what happens when we guess more than $3$ numbers? Are the rolled numbers different? Thanks. – 2012-11-11
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0Hi, yes they are different and we quess 5 numbers (if at least 3 of them were rolled in lottery we won the third price) – 2012-11-11
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0Check the comment of Ross Millikan, he did the question assuming you need to get exactly $3$ right. Do similarily for exactly $4$ right and exactly $5$ right. Then you get total no of favourable outcomes. Alternatively, find the complementary probability, i.e getting less than $3$ as that would be easier.. – 2012-11-11
2 Answers
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Hint: There are ${ 35 \choose 5}$ total draws. To get specifically third prize, you need to select $3$ of your $5$ and $2$ of the other $30$.
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0OK so I get C(3,5)*C(2,30)/C(5,35) but why do I write *C(2,30)? – 2012-11-11
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0@user12392: I had assumed that if you get four you win second prize and if you get all five you get first prize. But this approach is fine to get those chances, too. I agree with your calculation for three. – 2012-11-11
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0@user12392: for the ${30 \choose 2}$ see André Nicolas' comment to the other answer. He gives some good examples. – 2012-11-11
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Choose 5 from 35 in $\binom{35}{5}$ and from 5 numbers to get 3 exists $\binom{5}{3}=10$ possibilities and 2 other numbers you choose from 30 others thats not are in your ticket in $\binom{30}{2}=435 $ ways so total ways to win third place is $10\times435=4350$ ways.
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0Although it is true ${5 \choose 2}={5 \choose 3}$ I think it is easier to see where ${5 \choose 3}$ comes from. – 2012-11-11
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0Why do I choose 2 other numbers from 30 others that are not in my ticket? – 2012-11-11
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1There are many many tickets that will get you a third prize. If the numbers drawn are $1,2,3,4,5$, you will win third prize with $2,3,4, 7,11$ but also with $2,3,4, 12,20$ and with $2,3,4, 31,33$, and so on. – 2012-11-11