1. A bag contains red, blue, green, and yellow marbles. Seth takes a marble from the bag without looking, records the color of the marble, and then puts the marble back in the bag. He repeats the process until he has recorded the colors of 35 marbles. The chart below shows the results of his experiment.
outcome: red blue green yellow
frequency:10 5 13 7
Use the results of this experiment to find each probability. Write each answer as a fraction in lowest terms.
a. Find the experimental probability that the next marble he chooses is yellow.
b. Find the experimental probability that the next marble he chooses is either blue or red.
Experimental probability
=(observed frequency)/size of sample space
which leads to
P(red)=10/35=2/7
P(blue)=5/35=1/7
... etc
also, since these probabilities are complementary, we can conclude that P(blue or red)=P(blue)+P(red)
Try to work out the numbers and post for checking if you wish.
To find the experimental probability, we divide the frequency of the desired outcome by the total number of trials.
a. The frequency of yellow marbles is 7, and the total number of trials is 35.
So, the experimental probability of choosing a yellow marble is 7/35.
b. To find the experimental probability of choosing either a blue or a red marble, we add their frequencies (5 + 10) and divide by the total number of trials.
The total frequency of blue and red marbles is 15, and the total number of trials is 35.
Therefore, the experimental probability of choosing either a blue or a red marble is 15/35.
Note: It is important to understand that experimental probability is based on observed data from a limited number of trials. As the number of trials increases, the experimental probability tends to converge toward the theoretical probability.