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Adeoti threw a fair dice 250 times and got the following frequency table. Find the relative frequency of throwing a 4, an even number, and throwing a 3 or 5.

Mathematics

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Answers

3 parts
a

21125\frac{21}{125}

b

127250\frac{127}{250}

c

83250\frac{83}{250}

Step-by-step solution

9 steps

Here are the relative frequencies:

The total number of trials is 250.
The formula for relative frequency is:

Relative Frequency=Number of successful trialsTotal number of trials\text{Relative Frequency} = \frac{\text{Number of successful trials}}{\text{Total number of trials}}

Part a· 3 steps

Find the relative frequency of throwing a 4.

  1. Identify the frequency of throwing a 4.

    From the table, the frequency of throwing a 4 is 42.

  2. Calculate the relative frequency.

    Relative Frequency (4)=Frequency of 4Total number of trials=42250\text{Relative Frequency (4)} = \frac{\text{Frequency of 4}}{\text{Total number of trials}} = \frac{42}{250}

  3. Simplify the fraction.

    42250=42÷2250÷2=21125\frac{42}{250} = \frac{42 \div 2}{250 \div 2} = \frac{21}{125}

    The relative frequency of throwing a 4 is 21125\boxed{\frac{21}{125}}.

Part b

127250\frac{127}{250}

Find the relative frequency of throwing an even number.

  1. Identify the frequencies of even numbers.

    The even numbers on a die are 2, 4, and 6.
    Frequency of 2 = 43
    Frequency of 4 = 42
    Frequency of 6 = 42

  2. Calculate the total frequency of throwing an even number.

    Frequency (even number)=43+42+42=127\text{Frequency (even number)} = 43 + 42 + 42 = 127

  3. Calculate the relative frequency.

    Relative Frequency (even number)=Frequency (even number)Total number of trials=127250\text{Relative Frequency (even number)} = \frac{\text{Frequency (even number)}}{\text{Total number of trials}} = \frac{127}{250}

    The relative frequency of throwing an even number is 127250\boxed{\frac{127}{250}}.

Part c

83250\frac{83}{250}

What is the relative frequency of throwing a 3 or 5.

  1. Identify the frequencies of throwing a 3 or 5.

    Frequency of 3 = 40
    Frequency of 5 = 43

  2. Calculate the total frequency of throwing a 3 or 5.

    Frequency (3 or 5)=40+43=83\text{Frequency (3 or 5)} = 40 + 43 = 83

  3. Calculate the relative frequency.

    Relative Frequency (3 or 5)=Frequency (3 or 5)Total number of trials=83250\text{Relative Frequency (3 or 5)} = \frac{\text{Frequency (3 or 5)}}{\text{Total number of trials}} = \frac{83}{250}

    The relative frequency of throwing a 3 or 5 is 83250\boxed{\frac{83}{250}}.

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