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What is the probability of selecting a number that is (m) even, (q) a multiple of 2, (n) odd, (p) prime, (r) composite, (s) a prime factor of 4.

Mathematics

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Answer

12\mathbf{\frac{1}{2}}

Step-by-step solution

4 steps

To answer this question, we need to know the set of numbers from which a selection is made. Since this information is not provided in the image, we will assume the standard context for such problems: selecting a number from a fair six-sided die.

Assumption: The numbers are selected from the set {1,2,3,4,5,6}\{1, 2, 3, 4, 5, 6\}.
The total number of possible outcomes is 6.

The question asks for the probability of selecting a number that is "prime", as indicated by the checkmark next to option (p).

  1. Identify the sample space.

    The sample space SS consists of the numbers on a standard six-sided die:

    S={1,2,3,4,5,6}S = \{1, 2, 3, 4, 5, 6\}

    The total number of outcomes is ∣S∣=6|S| = 6.

  2. Identify the favorable outcomes for selecting a prime number.

    A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself.
    From the sample space SS:

    • 1 is not a prime number.
    • 2 is a prime number (divisors: 1, 2).
    • 3 is a prime number (divisors: 1, 3).
    • 4 is not a prime number (divisors: 1, 2, 4).
    • 5 is a prime number (divisors: 1, 5).
    • 6 is not a prime number (divisors: 1, 2, 3, 6). The prime numbers in the sample space are {2,3,5}\{2, 3, 5\}. The number of favorable outcomes is 3.

  3. Calculate the probability.

    The probability of an event is given by the formula:

    P(event)=Number of favorable outcomesTotal number of possible outcomesP(\text{event}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} P(prime)=36P(\text{prime}) = \frac{3}{6}

  4. Simplify the probability.

    P(prime)=12P(\text{prime}) = \frac{1}{2}

    The probability of selecting a prime number is 12\mathbf{\frac{1}{2}}.

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