Two even numbers are selected from the first ten even numbers not including zero. What's the probability that the sum of these two numbers is 30.

My instructor said 3/10. Is this really correct?

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    $\begingroup$ Selected in what way? With equal probability? With replacement or without replacement? Did you try listing out the possible pairs of numbers? $\endgroup$ – Glen_b Oct 23 '17 at 23:14

There are 6 ways to select a tuple such that it adds up to 30 and overall 10*9 tuples (without replacement, 10*10 with). Therefore the asked probabilty should be 6/90 = 1/15. This is assuming that sample (i, j) is different from (i, j) (otherwise 45 options in total and only 3 tuples with the desired property -> gives again P=1/15)

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  • $\begingroup$ For sampling with replacement,. why do you divide by 90 rather than 100 (= 10*10)? $\endgroup$ – Mark L. Stone Oct 24 '17 at 11:59
  • $\begingroup$ As I wrote: for sampling with replacement you should use 10*10. Excuse me if that was formulated not clear enough. $\endgroup$ – Jojo Oct 24 '17 at 12:03

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