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