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Of the $12$ people who have taken their seats at a seminar, $2$ have red hair. What is the experimental probability that the next person to take a seat will have red hair? Simplify your answer and write it as a fraction or whole number. $\newline$ $P(\text{red}) = \_\_$

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Experimental probability

Full solution

Q. Of the

12

people who have taken their seats at a seminar,

2

have red hair. What is the experimental probability that the next person to take a seat will have red hair? Simplify your answer and write it as a fraction or whole number.

\newline

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

Understand concept: Understand the concept of experimental probability. Experimental probability is calculated based on the outcomes of an experiment or past event. In this case, the experiment is the $12$ people who have already taken their seats, and we are interested in the characteristic of having red hair.
Calculate probability: Calculate the experimental probability. The experimental probability of an event is given by the ratio of the number of times the event has occurred to the total number of trials or instances. Here, the event is ＂a person having red hair＂ and the number of trials is ＂the number of people who have taken their seats,＂ which is $12$ .
Use given information: Use the given information to find the probability. We know that $2$ out of the $12$ people who have taken their seats have red hair. Therefore, the experimental probability, $P(\text{red})$ , is $2$ out of $12$ .
Simplify the fraction: Simplify the fraction. The fraction $\frac{2}{12}$ can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is $2$ . $\newline$ $P(\text{red}) = \frac{2}{12} = \left(\frac{2 \div 2}{12 \div 2}\right) = \frac{1}{6}$

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