The probability for an individual particle to have not yet decayed after a time t since its

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The probability for an individual particle to have not yet decayed after a time t since its creation is given by prob(t) =  e-t/τ, where t is the mean lifetime of the particle. 

(a) What is the probability that a  π+ at rest will still exist after 0.10 ms? 

(b) What is the probability that a π+ of momentum 500 MeV/c can travel a distance of 20 m before decaying? Consider time dilation. 

(c) What is the probability that a φ particle with the same momentum could travel the same distance?

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