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A spinner is spun 100 times. The results are shown in the table below. Calculate the experimental probability of spinning an 8, a 5, and a 7.

Mathematics

ScanSolve AI Answer

Step-by-step solution

5 steps
  1. Find the missing value 'q'.

    The total number of trials is 100. The sum of all successful outcomes must equal the total number of trials.

    q+18+15+16+12+7+10+13=100q + 18 + 15 + 16 + 12 + 7 + 10 + 13 = 100 q+91=100q + 91 = 100 q=100−91q = 100 - 91 q=9q = 9
  2. Calculate the experimental probability for spinning an 8.

    The number of successful outcomes for spinning an 8 is 13. The total number of trials is 100.

    P(spinner spins an 8)=Number of times 8 was spunTotal number of trialsP(\text{spinner spins an 8}) = \frac{\text{Number of times 8 was spun}}{\text{Total number of trials}} P(spinner spins an 8)=13100=0.13P(\text{spinner spins an 8}) = \frac{13}{100} = 0.13

    As a percentage: 0.13×100%=13%0.13 \times 100\% = 13\%
    The experimental probability is 0.13 or 13%\boxed{\text{0.13 or 13\%}}.

  3. Calculate the experimental probability for spinning a 5.

    The number of successful outcomes for spinning a 5 is 12. The total number of trials is 100.

    P(spinner spins a 5)=Number of times 5 was spunTotal number of trialsP(\text{spinner spins a 5}) = \frac{\text{Number of times 5 was spun}}{\text{Total number of trials}} P(spinner spins a 5)=12100=0.12P(\text{spinner spins a 5}) = \frac{12}{100} = 0.12

    As a percentage: 0.12×100%=12%0.12 \times 100\% = 12\%
    The experimental probability is 0.12 or 12%\boxed{\text{0.12 or 12\%}}.

  4. Calculate the experimental probability for spinning a 7.

    The number of successful outcomes for spinning a 7 is 10. The total number of trials is 100.

    P(spinner spins a 7)=Number of times 7 was spunTotal number of trialsP(\text{spinner spins a 7}) = \frac{\text{Number of times 7 was spun}}{\text{Total number of trials}} P(spinner spins a 7)=10100=0.10P(\text{spinner spins a 7}) = \frac{10}{100} = 0.10

    As a percentage: 0.10×100%=10%0.10 \times 100\% = 10\%
    The experimental probability is 0.10 or 10%\boxed{\text{0.10 or 10\%}}.

  5. Calculate the experimental probability for spinning 1 and 4.

    This means spinning a 1 OR spinning a 4.
    The number of successful outcomes for spinning a 1 is 9.
    The number of successful outcomes for spinning a 4 is 16.
    The total number of successful outcomes for spinning 1 or 4 is 9+16=259 + 16 = 25.
    The total number of trials is 100.

    P(spinner spins 1 or 4)=Number of times 1 or 4 was spunTotal number of trialsP(\text{spinner spins 1 or 4}) = \frac{\text{Number of times 1 or 4 was spun}}{\text{Total number of trials}} P(spinner spins 1 or 4)=25100=0.25P(\text{spinner spins 1 or 4}) = \frac{25}{100} = 0.25

    As a percentage: 0.25×100%=25%0.25 \times 100\% = 25\%
    The experimental probability is 0.25 or 25%\boxed{\text{0.25 or 25\%}}.

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