+0  
 
0
107
2
avatar+252 

a.) What is the expected value of the number shown when we draw a single slip of paper?

b.) What is the expected value of the number shown if we add one additional 4 to the bag?

c.) What is the expected value of the number shown if we add two additional 4's (instead of just one) to the bag?

d.) How many 4's do we have to add to make the expected value equal to 3?

Lightning  Mar 29, 2018
 #1
avatar+26724 
+2

a.) What is the expected value of the number shown when we draw a single slip of paper?

 

E = (8*2 + 2*4)/(8 + 2) → 2.4

 

b.) What is the expected value of the number shown if we add one additional 4 to the bag?

 

E = (8*2 + 3*4)/(8 + 3) → 2.545...

 

Now try c) and d) yourself.

Alan  Mar 29, 2018
 #2
avatar+86944 
+1

Thanks, Alan.....here's  the last two

 

c)

[ 8*2  + 4*4]  / [ 8 + 4 ]  = [ 16 + 16] / [ 12 ]   =  32/12  =  8/3  

 

d) We need to solve this for N

 

[ 8*2  + N*4] / [ 8  + N ]  =  3

 

[ 16 + 4N]  =  3 [ 8 + N ]

 

16 + 4N  =  24 + 3N  

 

N  =  8  ⇒  number of 4's  we need to have to have an expected value of 3

 

So....we need to add N - 2  =   8 - 2   =   6 

 

 

cool cool cool 

CPhill  Mar 29, 2018

15 Online Users

avatar
avatar

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.