A basket contains 5 red and 2 white identical ball. A ball is drawn from the basket at random, calculate the probability that it is either white or red

Mathematics

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1

Step-by-step solution

4 steps

  1. Determine the total number of balls in the basket.

    There are 5 red balls and 2 white balls.
    Total number of balls = 5+2=75 + 2 = 7 balls.

  2. Calculate the probability of drawing a red ball.

    The number of red balls is 5.

    P(Red)=Number of red ballsTotal number of balls=57P(\text{Red}) = \frac{\text{Number of red balls}}{\text{Total number of balls}} = \frac{5}{7}

  3. Calculate the probability of drawing a white ball.

    The number of white balls is 2.

    P(White)=Number of white ballsTotal number of balls=27P(\text{White}) = \frac{\text{Number of white balls}}{\text{Total number of balls}} = \frac{2}{7}

  4. Calculate the probability of drawing either a white or a red ball.

    Since drawing a red ball and drawing a white ball are mutually exclusive events (a ball cannot be both red and white), the probability of drawing either is the sum of their individual probabilities.

    P(White or Red)=P(White)+P(Red)P(\text{White or Red}) = P(\text{White}) + P(\text{Red}) P(White or Red)=27+57=2+57=77=1P(\text{White or Red}) = \frac{2}{7} + \frac{5}{7} = \frac{2+5}{7} = \frac{7}{7} = 1

    This means it is certain that any ball drawn will be either white or red, as there are no other colors of balls in the basket.

    The probability that it is either white or red is 1.

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