4.36 Reflection of neutron particles. Refer to the neutral particle transport pr

Question

4.36 Reflection of neutron particles. Refer to the neutral particle transport problem described in Exercise 3.42 (p. 84). Re call that particles released into an evacuated duct collide with the inner duct wall and are either scattered (reflected) with probability .16 or absorbed with probability .84. a. If 4 particles are released into the duct, what is the probability that all 4 will be absorbed by the inner duct wall? Exactly 3 of the 4? b. If 20 particles are released into the duct, what is the prob ability that at least 10 will be reflected by the inner duct wall? Exactly 10? A P7 Orannot

Explanation / Answer

a. Probability that a particle is absorbed by the inner wall

= 0.84

=> Probability that all 4 particles will be absorbed into the inner wall

= (0.84)4

= 0.4978

There are 4C3 ways to choose the 3 particles that are absorbed into the inner wall.

Probability that a particle won't be absorbed into the inner wall = 0.16

=> Probability that exactly 3 particles will be absorbed into the inner wall

= 4C3 * (0.84)3 * 0.16

= 4 * 0.592704 * 0.16

= 0.3793

b. The 10 particles can come in 20C10 ways.

Probability that EXACTLY 10 particles are reflected into the inner wall

= 20C10 * (0.84)10 * (0.16)10

= 0.000355

The probability that atleast 10 will be reflected

= 20C10 * (0.84)10 * (0.16)10 + 20C11 * (0.84)9 * (0.16)11 + 20C12 * (0.84)8 * (0.16)12 + 20C11 * (0.84)7 * (0.16)13 + ..... 20C20 * (0.84)0 * (0.16)20

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