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# Probability

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In a bag with $20$ marbles, five of them are blue. How many blue marbles must be added to the bag so that the probability of selecting a blue marble at random is $\frac{5}{8}$?

Aug 5, 2023

#2
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Let   B  be the number of blue matbles that we need to  add

So

Total Blue  / Total Number of marbles =   5/8

[5 + B ] / [ 20 + B ]   = 5/8

5 + B =  (5/8) ( 20 + B]    nultiply both sides by 8/5

8 + (8/5) B  = 20 + B

(8/5)B - B = 20 - 8

(3/5)B = 12

B = 12 * (5/3)  =  60 / 3 =  20

We need to add 20 blue marbles

Proof

[5 + 20 ] / [ 20 + 20]  =  25 / 40  =  5 / 8   Aug 5, 2023

#2
+1

Let   B  be the number of blue matbles that we need to  add

So

Total Blue  / Total Number of marbles =   5/8

[5 + B ] / [ 20 + B ]   = 5/8

5 + B =  (5/8) ( 20 + B]    nultiply both sides by 8/5

8 + (8/5) B  = 20 + B

(8/5)B - B = 20 - 8

(3/5)B = 12

B = 12 * (5/3)  =  60 / 3 =  20

We need to add 20 blue marbles

Proof

[5 + 20 ] / [ 20 + 20]  =  25 / 40  =  5 / 8   CPhill Aug 5, 2023