A jar contains 8 red marbles numbered 1 to 8 and 7 blue marbles numbered 1 to 7. A marble is drawn at random from the jar. Find the probabil

Question

A jar contains 8 red marbles numbered 1 to 8 and 7 blue marbles numbered 1 to 7. A marble is drawn at random from the jar. Find the probability that the marble is blue or even-numbered.

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Hadley 3 weeks 2021-09-27T00:45:31+00:00 1 Answer 0

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    2021-09-27T00:47:00+00:00

    Answer:

    Therefore the probability that the marble is blue or even numbered is \frac{11}{15}

    Step-by-step explanation:

    Probability: The ratio of favorable outcomes to the total outcomes.

    It is denoted by P.

    Probability= \frac{\textrm{favorable outcomes}}{\textrm{Total outcomes}}

    Given that a jar contains 8 red marbles and 7 blue marbles.

    Total number of marbles = (8+7) = 15

    Let A = Event of getting a blue marble

    B= Event of getting of even marble.

    Even number blue marbles are 2, 4,6

    Even number red marbles are 2, 4,6,8

    The number of even marbles are =(3+4)=7

    The probability of getting a blue marble is P(A)

    =\frac{\textrm{Total number of blue marbles}}{\textrm{Total number of blue marbles}}

    =\frac{7}{15}

    The probability of getting a even marble  is P(B)

    =\frac{\textrm{The number of even number marbles}}{\textrm{Total number of marbles}}

    =\frac{7}{15}

    The probability of getting a even numbered blue marble P(A∩B)

    =\frac{3}{16}

    P(blue marble or even- numbered)

    =P(A∪B)

    =P(A)+P(B)-P(A∩B)

    =\frac{7}{15} +\frac{7}{15}-\frac{3}{15}

    =\frac{11}{15}

    Therefore the probability that the marble is blue or even numbered is \frac{11}{15}

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