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turtle turtle

Binomial probability question please help!!

Hi, the question is:

5% of computer processors are defective. Processors are selected at random and put into packs of 15.

(b) Two packets are selected at random. Find the probability that there are at least two defective processors in either packet

 

please help, thanks so much!!

 

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Posted (edited)

@turtle turtle 
X ~ B(15, 0.05), where X is number of defects

First find probability that a single packet has at least two defects. P(X >= 2) = 1 - P(X=0) - P(X=1) = 1 - (0.95)15 - 15(0.95)14(0.05) = 0.17095
then make a new distribution for SUCH packets

Y ~ B(2, 0.17095), where Y is the number of Packets. A Packet is a packet with at least two defective processors.

I am not too sure what "either packet" means. It can mean exactly one packet, at least one packet, or two packets. 
Respectively, you would find P(Y = 1), P(Y >= 1), or P(Y = 2) depending on the correct interpretation of the problem. 



 

Edited by kw0573
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4 hours ago, kw0573 said:

@turtle turtle 
X ~ B(15, 0.05), where X is number of defects

First find probability that a single packet has at least two defects. P(X >= 2) = 1 - P(X=0) - P(X=1) = 1 - (0.95)15 - 15(0.95)14(0.05) = 0.17095
then make a new distribution for SUCH packets

Y ~ B(2, 0.17095), where Y is the number of Packets. A Packet is a packet with at least two defective processors.

I am not too sure what "either packet" means. It can mean exactly one packet, at least one packet, or two packets. 
Respectively, you would find P(Y = 1), P(Y >= 1), or P(Y = 2) depending on the correct interpretation of the problem. 



 

Hi thanks so much for the reply!! Yeah, I was really confused about the word 'either' and after looking at the answer (0.0292) you're right, it means that both of them have to be greater than/equal to 2. Is it always the case that either means both, because it's really ambiguous? ty again :)

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3 hours ago, turtle turtle said:

Hi thanks so much for the reply!! Yeah, I was really confused about the word 'either' and after looking at the answer (0.0292) you're right, it means that both of them have to be greater than/equal to 2. Is it always the case that either means both, because it's really ambiguous? ty again :)

In my experience IB has typically been quite clear in these directions in math, especially because it can lead to different answers. 

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