Q:

Sofia tosses a bottle cap to see how it lands. She repeats this experiment 60 times and records the results in this table. Landing Position Times Result Occurred top up 9 top down 48 on its side 3 Which statement is true based on the results in the table? A. All of the outcomes are not equally likely because there is a lot of variation in their relative frequencies. B. All of the outcomes are equally likely because the relative frequencies of the cap landing top up and on its side do not vary much. C. All of the outcomes are equally likely because their relative frequencies are multiples of 3. D. All of the outcomes are not equally likely because the relative frequency of the cap landing on its side is the lowest.

Accepted Solution

A:
Answer:A. All of the outcomes are not equally likely because there is a lot of variation in their relative frequencies.Step-by-step explanation:There are 2 ways to find the probability of an event: theoretical calculation or experimentation. In this case Sofia uses the experimental method. Therefore she must repeat the experiment of throwing the lid a number of times n. Where n must be a large number to get more accurate results. When a series of events are equally likely, then, for a number of trials, the frequency of occurrence of each event should be similar. On the other hand, if the frequency of occurrence of the events is significantly different, it can be concluded that the events do not have the same probability of occurrence. In this experiment, the relative frequencies are: [tex]\frac{9}{60}[/tex] times for top up [tex]\frac{48}{60}[/tex] times for top down [tex]\frac{3}{60}[/tex]  times for it's side Note that the frequencies are significantly different for the 60 trials, so: All of the outcomes are not equally likely