The number of red balls in a bag is 10 more than the number of black balls. If the probability of drawing a red ball at random from this bag is $\frac{3}{5}$, then the total number of balls in the bag

Question

The number of red balls in a bag is 10 more than the number of black balls. If the probability of drawing a red ball at random from this bag is $\frac{3}{5}$, then the total number of balls in the bag is:

Accepted Answer

Step 1: Let black $= b$, red $= b + 10$, total $= 2b + 10$. $\frac{b+10}{2b+10} = \frac{3}{5} \Rightarrow 5b + 50 = 6b + 30 \Rightarrow b = 20$. Total $= 50$.

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