Probility

2008-09-03 9:12 pm
Dear All,

Please Help!

Assume that in any batch of soft drink bottles 25% are defective.

a) If we take a sample of 5 bottles from a case of 24, what is the chance that exactly 3 will be defective?

b) If we take a sample of 5 bottles from a case of 24, what is the chance that at least one will be defective?

c) If we take a sample of 5 bottles from a shelf with many, many bottles on it, what is the chance that exactly 3 will be defective?

d) If we take a sample of 5 bottles from a shelf with many, many bottles on it, what is the chance that at least one will be defective?

e) If we take a sample of 100 bottles from a shelf with many, many bottles on it, what is the chance that at least 25 will be defective?

f) If we take a sample of 100 bottles from a shelf with 500 bottles on it, what is the chance that a least 25 will be defective>
更新1:

please show the formula to me, I hard to understand. Thank you

回答 (1)

2008-09-03 10:57 pm
✔ 最佳答案
(a) Pr[3 defective] = (6C3)(18C2)/(24C5) = 255/3542

(b) Pr[at least one defective]
= 1 - Pr[no defective]
= 1 - (18C5)/(24C5) = 202/253

(c) Pr[3 defective] = (5C3) x (0.25^3) x (0.75^2) = 45/512

(d) Pr[at least one defective] = 1 - (0.75^5) = 781/1024

(e)
We approximate using normal distribution
Let X = number of defective bottles
X ~ N(100x0.25, 100x0.25x0.75)
Pr[X>=25]
=Pr[z>(25-25-0.5/sqrt(18.75))]
=Pr[z>-0.1155]
=0.5460

(f) I'd do the same as part (e) - but I'm not sure about this one


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