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During a period of 79 days he arrives at school on time at 53 occasions. Estimate the probability that Paulo arrives on time.

Mathematics

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Answer

5379\frac{53}{79}

0.671

Step-by-step solution

4 steps

  1. Identify the total number of trials.

    Paulo's arrival was observed over a period of 79 days. So, the total number of trials is 79.

  2. Identify the number of favorable outcomes.

    Paulo arrived on time on 53 occasions. This is the number of favorable outcomes.

  3. Calculate the probability.

    The probability of an event is estimated by the ratio of the number of times the event occurred to the total number of trials.

    P(arrives on time)=Number of times Paulo arrived on timeTotal number of daysP(\text{arrives on time}) = \frac{\text{Number of times Paulo arrived on time}}{\text{Total number of days}} P(arrives on time)=5379P(\text{arrives on time}) = \frac{53}{79}

  4. Express the probability as a decimal (optional, but often preferred for probabilities).

    P(arrives on time)≈0.670886...P(\text{arrives on time}) \approx 0.670886...

    Rounding to a reasonable number of decimal places, e.g., three decimal places:

    P(arrives on time)≈0.671P(\text{arrives on time}) \approx 0.671

    The estimated probability that Paulo arrives on time is 5379\boxed{\frac{53}{79}} or approximately 0.671\boxed{0.671}.

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