Question

There are two bags Bag I and Bag II. Bag I contains 3 red balls and 7 blue balls, whereas Bag II contains total 40 balls. If the probability of drawing a blue ball from bag I is 4+3 times the probability of drawing a blue ball from bag II, then number of blue balls in bag II is

Answer 1

Dear Student,

$$\begin{gathered} \mathrm{Probability}\mathrm{of}\mathrm{drawing}\mathrm{a}\mathrm{blue}\mathrm{ball}\mathrm{from}\mathrm{bag}1=\frac{7}{10} \\ \mathbf{Given}\mathbf{:}\mathbf{\hspace{0.17em}}\mathrm{Total}\mathrm{number}\mathrm{of}\mathrm{balls}\mathrm{in}\mathrm{bag}2=40 \\ \mathrm{Let}\mathrm{the}\mathrm{number}\mathrm{of}\mathrm{blue}\mathrm{balls}\mathrm{in}\mathrm{Bag}2\mathrm{is}\mathrm{x}. \\ \mathrm{Then},\mathrm{probability}\mathrm{of}\mathrm{drawing}\mathrm{blue}\mathrm{ballfrom}\mathrm{bag}2=\frac{\mathrm{x}}{40} \\ \mathrm{According}\mathrm{to}\mathrm{question},\frac{\mathrm{x}}{40}=\left(4+3\right)\times \frac{7}{10} \\ \frac{\mathrm{x}}{40}=7\times \frac{7}{10} \\ \frac{\mathrm{x}}{40}=\frac{1}{10} \\ \boxed{\mathbf{x}\mathbf{=}\mathbf{4}} \\ \mathrm{So},\mathrm{there}\mathrm{are}4\mathrm{blue}\mathrm{balls}\mathrm{in}\mathrm{bag}2. \end{gathered}$$

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