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Problem statement

A particle has a $4/7$ chance of hitting a nucleus, in which case the particle disappears, and three identical particles appear in its place. The particle has a $3/7$ chance of disappearing without bumping into any nucleus. Determine the probability of an explosion if the reaction starts with a single particle.

To ensure you have all the info I have:

Relevant information

Jump chain and holding times

Explosion

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    What have you tried? Where are you getting stuck? What don't you understand? Tell us! – 2017-02-27
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    Thank you for reply . I haven't found a blueprint for the solution. I don't understand how this chemical reaction translates into an application of the defined term "explosion" - I think I just need a small hint to get me on my way – 2017-02-27

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