High School

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A car rental agency has 4 minivans and 8 other vehicles available. What is the probability that a randomly selected vehicle will be a minivan? Write your answer as a fraction or whole number.

P(minivan) =

Answer :

To find the probability that a randomly selected vehicle will be a minivan, we need to understand the basic concept of probability. Probability is the measure of how likely an event is to occur and is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.

Step-by-Step Solution:


  1. Identify the Total Number of Vehicles:
    The car rental agency has a total of 4 minivans and 8 other vehicles.
    Therefore, the total number of vehicles is calculated as follows:

    [tex]\text{Total Vehicles} = 4 + 8 = 12[/tex]


  2. Identify the Number of Favorable Outcomes:
    The favorable outcome in this case is selecting a minivan. Since there are 4 minivans available, the number of favorable outcomes is 4.


  3. Calculate the Probability:
    The probability [tex]P[/tex] of selecting a minivan is given by the formula:

    [tex]P(\text{minivan}) = \frac{\text{Number of Favorable Outcomes}}{\text{Total Number of Possible Outcomes}}[/tex]

    Substituting the values we have:

    [tex]P(\text{minivan}) = \frac{4}{12}[/tex]


  4. Simplify the Fraction:
    To simplify [tex]\frac{4}{12}[/tex], we divide both the numerator and the denominator by their greatest common divisor, which is 4:

    [tex]P(\text{minivan}) = \frac{4 \div 4}{12 \div 4} = \frac{1}{3}[/tex]



Therefore, the probability that a randomly selected vehicle will be a minivan is [tex]\frac{1}{3}[/tex].

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