Question

1. Suppose you have just received a shipment of 100 iPads where 7 iPads are defective. To determine whether or not you will accept the shipment, you randomly select 3 iPads and test them. If all 3 of the tablets works, you accept the shipment, if not, you reject it. What is the probability of rejecting the shipment

Answer 1

Answer:

$p(x\geq 1)=0.1975$

Step-by-step explanation:

the probability that x iPads are defective in the sample follows a hypergeometric distribution, so it is calculated as:

$p(x)=\frac{kCx*((N-k)C(n-x))}{NCn}$

Where $aCb=\frac{a!}{b!(a-b)!}$

Because we have a N elements with k elements that are defective and we are going to take a sample of n elements. So, replacing N by 100, k by 7 and n by 3, we get:

$p(x)=\frac{7Cx*((100-7)C(3-x))}{100C3}$

Now, the probability of rejecting the shipment is the probability that at least one iPad of the sample is defective, so:

$p(x\geq 1)=p(1)+p(2)+p(3)$

Then:

$p(1)=\frac{7C1*((100-7)C(3-1))}{100C3}=0.1852\\p(2)=\frac{7C2*((100-7)C(3-2))}{100C3}=0.0121\\p(3)=\frac{7C3*((100-7)C(3-3))}{100C3}=0.0002$

Finally, the probability of rejecting the shipment is:

$p(x\geq 1)=0.1852+0.0121+0.0002=0.1975$