Probability: A bag contains only red and blue marbles. Yasmine takes one marble...

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Sharon3431

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Nov 10, 2016
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5
Hi everyone.
I got the right answer to this, but only through experimentation. Eg 1 4 5; 2, 8, 10; 3, 12, 15; 4, 16, 20;
5, 20, 25; so adding 5 here to the Reds gives me the right fraction. Can someone please show me how to do this algebraically?
Thanks


A bag contains only red and blue marbles.
Yasmine takes one marble at random from the bag.The probability that she takes a red marble is
page42image2448
1/5.
Yasmine returns the marble to the bag and adds five more red marbles to the bag.The probability that she takes one red marble at random is now 1/3.


How many marbles of each colour were originally in the bag?
 
Sharon3431 said:
Hi everyone.
I got the right answer to this, but only through experimentation. Eg 1 4 5; 2, 8, 10; 3, 12, 15; 4, 16, 20;
5, 20, 25; so adding 5 here to the Reds gives me the right fraction. Can someone please show me how to do this algebraically?
Thanks


A bag contains only red and blue marbles.
Yasmine takes one marble at random from the bag.The probability that she takes a red marble is
page42image2448
1/5.
Yasmine returns the marble to the bag and adds five more red marbles to the bag.The probability that she takes one red marble at random is now 1/3.


How many marbles of each colour were originally in the bag?
Click to expand...
The P(red)= 1/5 could have come from 2/10 (meaning that there are 10 marbles with 2 being red) or could have come from 3/15 (meaning that there are 15 marbles with 3 being red)... or could have come from n/5n (meaning that there are 5n marbles with n being red).


After adding 5 more red marbles we know there are 5n+5 marbles and n+5 are red. Can you continue from here?
 
Sharon3431 said:
A bag contains only red and blue marbles.
Yasmine takes one marble at random from the bag.The probability that she takes a red marble is
page42image2448
1/5.
Yasmine returns the marble to the bag and adds five more red marbles to the bag.The probability that she takes one red marble at random is now 1/3.
How many marbles of each colour were originally in the bag?
Click to expand...
Solve these for \(\displaystyle R~\&~B\) in:
\(\displaystyle \dfrac{R}{R+B}=\dfrac{1}{5}\) AND \(\displaystyle \dfrac{R+5}{R+5+B}=\dfrac{1}{3}\).

Thanks Jomo
 
Last edited:
pka said:
Solve these for \(\displaystyle R~\&~B\) in:
\(\displaystyle \dfrac{R}{R+B}=\dfrac{1}{5}\) AND \(\displaystyle \dfrac{R}{R+5+B}=\dfrac{1}{3}\).
Click to expand...
Nice, but in the 2nd fraction the numerator should be R+5
 
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