5. Geophysicists determine the age of a zircon by counting the number ofuranium fission tracks on a polished surface. A particular zircon is of such anage that the average number of tracks per square centimeter is five. What is theprobability that a 2cm2sample of this zircon will reveal at most three tracks, thus leading to an underestimation of the age of the material

the probability that a 2cm² sample of the zircon will reveal at most three tracks is 0.0104

Step-by-step explanation:

Given that; 7

uranium fission tracks occur on average 5 per every square centimeter

i.e λ = 5

the required centimeter square s = 2

let X be the number of uranium fission tracks occur on the average per every square centimeter

therefore X follows poisson distribution

so the average number of tracks occur on 2-centimeter is;

k = λs

k = 5 × 2

k = 10

the required probability is;

P(x ≤ 3) = P( X=0 ) + P( X=1 ) + P( X=2 ) + P( X=3 )

= [ (e⁻¹⁰(10)⁰) / 0! ] + [ (e⁻¹⁰(10)¹) / 1! ] + [ (e⁻¹⁰(10)²) / 2! ] + [ (e⁻¹⁰(10)³) / 3! ]

= 0.00004 + 0.0005 + 0.0023 + 0.0076

= 0.0104

therefore the probability that a 2cm² sample of the zircon will reveal at most three tracks is 0.0104

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