Jenny has a bag with A, E, Q, and W letter tiles. She conducts a probability experiment. For each event in her experiment, Jenny randomly selects one tile from the bag, records the letter, and then replaces it. The results are shown in the table below.
Letter Frequency
A 6
E 12
Q 8
W 14
Will all the possible outcomes appear to be equally likely based on the observed frequencies?
What is the experimental probability for drawing a Q tile?
If there were a total of 70 tiles, what is the best estimate of the number of E tiles in the bag?
Based on the observed frequencies, it appears that all the possible outcomes are not equally likely. The letter E has the highest frequency, followed by W, Q, and A.
The experimental probability for drawing a Q tile can be calculated by taking the frequency of Q (8) divided by the total number of outcomes (6+12+8+14 = 40).
Experimental probability of drawing a Q tile = 8/40 = 1/5 = 0.2
If there were a total of 70 tiles, the best estimate of the number of E tiles in the bag can be calculated by taking the proportion of E tiles in the observed frequencies and scaling it up to 70 tiles.
Proportion of E tiles in the observed frequencies = 12/40 = 0.3
Estimated number of E tiles in a bag of 70 tiles = 0.3 * 70 = 21