You haven't told us if the first person cracks their egg before the rest of the people pick theirs...
Ding ding ding.
This is the crucial missing piece information.
Without knowing this, it would be reckless to commit to an answer.
If they all pick one after another without the previous person cracking the egg on their head, then yes, it's 1/6.
If they're playing russian roulette, then the chance of danger increases each time.. 1/6, 1/5, 1/4, 1/3, 1/2, goodnight Irene
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