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Binomial probability question please help!!


turtle turtle

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@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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