you are definitely correct.
Each ticket / number / combination… has the same chance of being the winning ticket. Buying 2 means you have twice that chance.
Of course, this is assuming that you are not blind picking the tickets, i.e. the 2 tickets bought have different numbers.
It could be that your colleague was referring to the fact that since the chance of winning is so so low (0.00000…%), doubling that has little to no effect
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