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Steve has three quarters, three nickels and three pennies. If Steve selects three coins at random and without replacement, what is the probability that the total value is exactly 35 cents? Express your answer as a common fraction.

 Apr 16, 2015

Best Answer 

 #5
avatar+118673 
+15

The only way you can get 35 cents is with 1 quarter and 2 nickels     (talk about funny money)

There are 3 ways to pick up a quarter  3C1

and there are 3 ways you can pick up 2 nickels   3C2

So there are  3*3=9 ways to choose 1 quarters and 2 nickels.   That is 9 favourable outcomes :)

Now, there are  9C3=84  ways to choose 3 coins from 9  SO

the prob of picking up 35c is     $${\frac{{\mathtt{9}}}{{\mathtt{84}}}} = {\frac{{\mathtt{3}}}{{\mathtt{28}}}} = {\mathtt{0.107\: \!142\: \!857\: \!142\: \!857\: \!1}}$$

 

Now does you online program agree this time Mellie?        

 Apr 16, 2015
 #1
avatar+129852 
+10

The possible amounts of money that could be made are

(25,25,25)  = 75 cents       (5,5,1) = 11 cents

(25, 25,5) = 55 cents         (5 ,1, 1) = 7 cents

(25,5,5)  = 35 cents           (25, 5 , 1)  = 31 cents

(5,5,5) = 15 cents              

(25, 25, 1) = 51 cents

(25,1, 1)  = 27 cents

(1,1,1)  = 3 cents

 

So 35 cents probability  =    1/10  

I think that's it   !!!

 

  

 Apr 16, 2015
 #2
avatar+1836 
0

Sorry that you worked so hard, but this answer is incorrect. 

 Apr 16, 2015
 #3
avatar+129852 
0

Let me look again, Mellie.....

 

  

 Apr 16, 2015
 #4
avatar+1836 
+5

Thanks you so much!!

 Apr 16, 2015
 #5
avatar+118673 
+15
Best Answer

The only way you can get 35 cents is with 1 quarter and 2 nickels     (talk about funny money)

There are 3 ways to pick up a quarter  3C1

and there are 3 ways you can pick up 2 nickels   3C2

So there are  3*3=9 ways to choose 1 quarters and 2 nickels.   That is 9 favourable outcomes :)

Now, there are  9C3=84  ways to choose 3 coins from 9  SO

the prob of picking up 35c is     $${\frac{{\mathtt{9}}}{{\mathtt{84}}}} = {\frac{{\mathtt{3}}}{{\mathtt{28}}}} = {\mathtt{0.107\: \!142\: \!857\: \!142\: \!857\: \!1}}$$

 

Now does you online program agree this time Mellie?        

Melody Apr 16, 2015
 #6
avatar+129852 
+5

Thanks, Melody......

 

 

  

 Apr 16, 2015
 #7
avatar+118673 
0

Thanks Chris and you are welcome,  BUT

Mellie hasn't said if her program agrees yet.  LOL

 

Anyway, probability is always fun, especially if you are convinced (rightly or wrongly) that you know what you are doing :))

Actually it is also fun when you understand what you did wrong and  why the correct answer is correct.  

 Apr 16, 2015
 #8
avatar+129852 
0

Eh....I wouldn't call it "fun"....but....I am learning.....[mainly....that I should avoid probability questions.....!!!! ]

 

  

 Apr 16, 2015
 #9
avatar+1836 
+5

It's correct!! Thanks Melody!!

 Apr 16, 2015
 #10
avatar+118673 
+5

Yea I am a genius.  

I just gotta get these halos off, I have two because I am double angelic.  

1 is strangling me and the other keeps tripping me over.   :/

 

Thanks by the way :)))

 Apr 16, 2015
 #11
avatar+129852 
0

OMG.....I think I'm going to be sick.....!!!!

Hope I don't throw up on one of your "halos" .......!!!!

 

  

 Apr 16, 2015
 #12
avatar+118673 
0

you are just jealous because you don't have any and I've got 2!

 Apr 16, 2015
 #13
avatar+129852 
0

Oops!!!!......I think I just got sick on that one you tripped over......might want to wash that thing off.....!!!!!

 

  

 Apr 16, 2015

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