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A bag contains a total of 30 red and blue balls. If a ball is randomly selected the probability of selecting a blue ball is 3/5. How many red balls are in the bag?

Mathematics

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Answer

12\text{12}

Step-by-step solution

4 steps

  1. Identify the total number of balls and the probability of selecting a blue ball.

    Total number of balls = 30
    Probability of selecting a blue ball, P(blue)=35P(\text{blue}) = \frac{3}{5}

  2. Use the probability formula to find the number of blue balls.

    The probability of an event is given by:

    P(event)=Number of favorable outcomesTotal number of outcomesP(\text{event}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}

    For selecting a blue ball:

    P(blue)=Number of blue ballsTotal number of ballsP(\text{blue}) = \frac{\text{Number of blue balls}}{\text{Total number of balls}}

    Substitute the given values:

    35=Number of blue balls30\frac{3}{5} = \frac{\text{Number of blue balls}}{30}

  3. Solve for the number of blue balls.

    Multiply both sides by 30:

    Number of blue balls=35×30\text{Number of blue balls} = \frac{3}{5} \times 30 Number of blue balls=3×6\text{Number of blue balls} = 3 \times 6 Number of blue balls=18\text{Number of blue balls} = 18

  4. Calculate the number of red balls.

    The bag contains only red and blue balls.

    Total number of balls=Number of red balls+Number of blue balls\text{Total number of balls} = \text{Number of red balls} + \text{Number of blue balls} 30=Number of red balls+1830 = \text{Number of red balls} + 18

    Subtract 18 from both sides:

    Number of red balls=30−18\text{Number of red balls} = 30 - 18 Number of red balls=12\text{Number of red balls} = 12

    The number of red balls in the bag is 12\text{12}.

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