are 3 defective items in a collection of 10 itemas. A sample of 8 itema is selec

Question

are 3 defective items in a collection of 10 itemas. A sample of 8 itema is selected randomly from the sample. Construct the probability mans function (pm) for X the group. Let the random variable X be the number of defective items in 5, Left handers account for nbout 12% of the general population. (a) In a random sample of 20 people, what in the probability the thero will be exactly 3 left handere? (b) What is the probability that exactly 20 people need to be randomly selected to observe exactly 3 left handers?

Explanation / Answer

4) P(X = 0) = 0

P(X = 1) = 3C1 * 7C7/10C8:= 3/45 = 1/15

P(X = 2 ) = 3C2 * 7C6 / 10C8 = 21/45 = 7/15

P(X =3) = 3C3 * 7C5 / 10C8 = 21/45 = 7/15

5) a) n = 20, p = 0.12

P(X = 3) = 20C3 * (0.13)^3 * (0.88)^17 = 0.2242

B) 19C2 * (0.12)^2 * (0.88)^17 * 0.12 = 0.0336

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