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A die is rolled. Calculate the probability that it will give (a) a five (b) a score less than 3 (c) an even number (d) a prime number.

Mathematics

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Step-by-step solution

3 steps

  1. Determine the total number of marbles in the bag.

    There are 3 black marbles and 1 white marble.
    Total number of marbles =3+1=4= 3 + 1 = 4.

  2. Identify the number of favorable outcomes (black marbles).

    Number of black marbles =3= 3.

  3. Calculate the probability of drawing a black marble.

    The probability is the ratio of the number of black marbles to the total number of marbles.

    P(black marble)=Number of black marblesTotal number of marbles=34P(\text{black marble}) = \frac{\text{Number of black marbles}}{\text{Total number of marbles}} = \frac{3}{4}

    The probability that the marble drawn is black is 34\boxed{\frac{3}{4}}.

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