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A piece of paper is drawn from a box containing slips of paper numbered 1 to 10. What is the experimental probability of drawing out 1, 6, an odd number, and a prime number?

Mathematics

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Answers

4 parts
a

110\frac{1}{10}

b

110\frac{1}{10}

c

12\frac{1}{2}

d

25\frac{2}{5}

Step-by-step solution

2 steps
  1. Identify the total number of possible outcomes.

    The numbers written on the pieces of paper are from 1 to 10.
    The set of possible outcomes is {1,2,3,4,5,6,7,8,9,10}\{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\}.
    The total number of possible outcomes is 10.
    Since no specific experimental results (frequencies) are provided, the experimental probability is calculated as the theoretical probability for this fair setup.

  2. Calculate the experimental probability for each case.

    The formula for probability is P(event)=Number of favorable outcomesTotal number of possible outcomesP(\text{event}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}.

    a) Drawing out 1
    The number of favorable outcomes (drawing the number 1) is 1.

    P(1)=110P(1) = \frac{1}{10}

    The experimental probability of drawing out 1 is 110\boxed{\frac{1}{10}}.

    b) Drawing out 6
    The number of favorable outcomes (drawing the number 6) is 1.

    P(6)=110P(6) = \frac{1}{10}

    The experimental probability of drawing out 6 is 110\boxed{\frac{1}{10}}.

    c) Drawing out an odd number
    The odd numbers between 1 and 10 are {1,3,5,7,9}\{1, 3, 5, 7, 9\}.
    The number of favorable outcomes is 5.

    P(odd number)=510=12P(\text{odd number}) = \frac{5}{10} = \frac{1}{2}

    The experimental probability of drawing out an odd number is 12\boxed{\frac{1}{2}}.

    d) Drawing out a prime number
    The prime numbers between 1 and 10 are {2,3,5,7}\{2, 3, 5, 7\}. (Note: 1 is not a prime number).
    The number of favorable outcomes is 4.

    P(prime number)=410=25P(\text{prime number}) = \frac{4}{10} = \frac{2}{5}

    The experimental probability of drawing out a prime number is 25\boxed{\frac{2}{5}}.

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