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Of the trains that recently pulled into Westford Station, $16$ were full and $4$ had room for more passengers. What is the experimental probability that the next train to pull in will be full? Simplify your answer and write it as a fraction or whole number. $\newline$ $P(\text{full}) = \_\_\_$

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Experimental probability

Full solution

Q. Of the trains that recently pulled into Westford Station,

16

were full and

4

had room for more passengers. What is the experimental probability that the next train to pull in will be full? Simplify your answer and write it as a fraction or whole number.

\newline

P(\text{full}) = \_\_\_

Define Experimental Probability: To find the experimental probability that the next train to pull into Westford Station will be full, we need to consider the number of times a full train has been observed in the past compared to the total number of trains observed. The formula for experimental probability is $P(\text{event}) = \frac{\text{Number of times event occurred}}{\text{Total number of trials}}$ .
Calculate Total Number: We are given that $16$ trains were full and $4$ had room for more passengers. To find the total number of trains observed, we add these two numbers together. $\newline$ Total number of trains $=$ Number of full trains $+$ Number of trains with room for more passengers $= 16 + 4 = 20$ .
Calculate Experimental Probability: Now we can calculate the experimental probability that the next train will be full by dividing the number of full trains by the total number of trains. $\newline$ $P(\text{full}) = \frac{\text{Number of full trains}}{\text{Total number of trains}} = \frac{16}{20}$ .
Simplify Fraction: To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is $4$ in this case. $\newline$ $P(\text{full}) = \frac{16}{4} / \frac{20}{4} = \frac{4}{5}.$

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