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Question
In a certain lottery 10,000 tickets are sold and ten equal prizes are awarded. What is the probability of not getting a prize if you buy two tickets.
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Solution
Number of tickets that are not getting a prize
= 10000 – 10
= 9990
∵ Total number of tickets = 10000
Number of ways of getting 2 tickets out of 9990 without prize = `""^9990C_2`
There are 10000 tickets in total.
Number of ways of getting 2 tickets out of them = `""^10000C_2`
Probability of getting two tickets with no prize = `(""^9990C_2)/(""^10000C_2)`.
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