A ball is drawn at random from a box containg 6 red balls, 4 white balls and 5 blue balls. What is the probability of getting: a) a red. b) a blue. c) a white. d) not white balls?

Mathematics

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Step-by-step solution

3 steps

Step 1: Determine the total number of balls in the box.
Number of red balls = 6
Number of white balls = 4
Number of blue balls = 5
Total number of balls = 6+4+5=156 + 4 + 5 = 15

Step 2: Calculate the probability of getting a red ball.

P(Red)=Number of red ballsTotal number of ballsP(\text{Red}) = \frac{\text{Number of red balls}}{\text{Total number of balls}} P(Red)=615P(\text{Red}) = \frac{6}{15} P(Red)=25P(\text{Red}) = \frac{2}{5}

Part a· 1 step

The probability of getting a red ball is 25\boxed{\frac{2}{5}}.

  1. Calculate the probability of getting 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}} P(Blue)=515P(\text{Blue}) = \frac{5}{15} P(Blue)=13P(\text{Blue}) = \frac{1}{3}

Part b· 1 step

The probability of getting a blue ball is 13\boxed{\frac{1}{3}}.

  1. Calculate the probability of getting a white ball.

    P(White)=Number of white ballsTotal number of ballsP(\text{White}) = \frac{\text{Number of white balls}}{\text{Total number of balls}} P(White)=415P(\text{White}) = \frac{4}{15}

Part c· 1 step

The probability of getting a white ball is 415\boxed{\frac{4}{15}}.

  1. Calculate the probability of not getting a white ball.

    The probability of not getting a white ball is 1 minus the probability of getting a white ball.

    P(Not White)=1−P(White)P(\text{Not White}) = 1 - P(\text{White}) P(Not White)=1−415P(\text{Not White}) = 1 - \frac{4}{15} P(Not White)=1515−415P(\text{Not White}) = \frac{15}{15} - \frac{4}{15} P(Not White)=1115P(\text{Not White}) = \frac{11}{15}

    Alternatively, the number of non-white balls is 6(red)+5(blue)=116 (\text{red}) + 5 (\text{blue}) = 11.

    P(Not White)=1115P(\text{Not White}) = \frac{11}{15}

Part d

The probability of not getting a white ball is 1115\boxed{\frac{11}{15}}.

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