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Of the last $12$ contestants on a game show, $3$ qualified for the bonus round. What is the experimental probability that the next contestant will qualify for the bonus round? Simplify your answer and write it as a fraction or whole number. $\newline$ $P(\text{bonus round}) = \_\_\_$

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Experimental probability

Full solution

Q. Of the last

12

contestants on a game show,

3

qualified for the bonus round. What is the experimental probability that the next contestant will qualify for the bonus round? Simplify your answer and write it as a fraction or whole number.

\newline

P(\text{bonus round}) = \_\_\_

Calculate Experimental Probability: The experimental probability is calculated by dividing the number of successful outcomes by the total number of trials. In this case, the successful outcomes are the contestants who qualified for the bonus round, and the total number of trials is the total number of contestants.
Identify Successful Outcomes: The number of contestants who qualified for the bonus round is $3$ , and the total number of contestants is $12$ .
Determine Total Number of Trials: To find the experimental probability, we divide the number of contestants who qualified ( $3$ ) by the total number of contestants ( $12$ ). $\newline$ P(bonus round) = Number of contestants who qualified / Total number of contestants $\newline$ P(bonus round) = $\frac{3}{12}$
Divide Successful Outcomes by Total Trials: We can simplify the fraction $\frac{3}{12}$ by dividing both the numerator and the denominator by their greatest common divisor, which is $3$ . $P(\text{bonus round}) = \frac{(3 \div 3)}{(12 \div 3)}$ $P(\text{bonus round}) = \frac{1}{4}$

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