Assume there are 10 dogs , 5 great danes and 5 labs. a. If the sampling...

Assume there are 10 dogs , 5 great danes and 5 labs.

a. If the sampling is done with replacement what is the probability that the 3rd great dane selected is the 4th 5th or 6th dog selected?

b. do the same assuming its done without replacement

Expert Solution

a)P( 3rd great dane selected is the 4th 5th or 6th dog selected)=P(2 out of first 3 are great dane and 4th is great dane)+P(2 out of first 4 are great dane and 5th is great dane)+P(2 out of first 5 are great dane and 6th is great dane)

=(³C₂(0.5)²*(0.5))*0.5+(⁴C₂(0.5)²*(0.5)²)*0.5+(⁵C₂(0.5)²*(0.5)³)*0.5=0.53125

b)

P( 3rd great dane selected is the 4th 5th or 6th dog selected)=P(2 out of first 3 are great dane and 4th is great dane)+P(2 out of first 4 are great dane and 5th is great dane)+P(2 out of first 5 are great dane and 6th is great dane)

=(⁵C₂*⁵C₁/¹⁰C₃)*(3/7)+(⁵C₂*⁵C₂/¹⁰C₃)*(3/6)+(⁵C₂*⁵C₃/¹⁰C₃)*(3/5)=(5/12)*(3/7)+(10/21)*(3/6)+(25/63)*(3/5) =0.654762

orchestra answered 2 years ago

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