Particles are suspended in a liquid medium at a concentration of 4 particles per mL. A large amount of the suspension is thoroughly agitated, and then 3 mL are withdrawn . Let $X$ be the number of the particles in the 3 mL. Answer the following:

a- The distribution of X is a Poisson distribution, what is its parameter ($\lambda$)?

b- Find the probability that no particle is withdrawn from the 3 mL.

c- Find the probability that one particle is withdrawn from the 3 mL.

  • $\begingroup$ I solved "a" as following but I do not know if it right or not : if there are 4 particles in 1 ml then there are 12 particles in 3 ml . but in this case should I consider the value 12 lambda ? $\endgroup$ Jun 3 '13 at 5:06
  • $\begingroup$ Please add the self-study tag and read the tag info. What do you know about Poisson distributions? $\endgroup$
    – Glen_b
    Jun 3 '13 at 5:55

a) Yes, you're correct, the value of $\lambda$ should be 12.

What have you done for the other two?

b and c both look right to me.

  • $\begingroup$ 'b' P(X=0) = e^-12 . (12)^0 / 0! = 6.144 x 10^-6 $\endgroup$ Jun 3 '13 at 6:53
  • $\begingroup$ "c" P(X=1)= (12)^1 . e^-12 / 1! = 7.37 x 10^-5 $\endgroup$ Jun 3 '13 at 6:54
  • $\begingroup$ Looks right ... $\endgroup$
    – Glen_b
    Jun 3 '13 at 7:49

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