Answer:
No, the three outcomes are not equally likely to occur.
Step-by-step explanation:
We have been given a table, which shows the three possible outcomes for how the cup will land: on its top, on its bottom, or on its side.
From our table we can see that cup lands on its top 4 times, on its bottom 1 time and on its side 25 times.
Let us find probability of each outcome.
[tex]\text{Probability}=\frac{\text{The number of favorable outcomes}}{\text{Total number of possible outcomes}}[/tex]
[tex]\text{Probability that cup will land on its top}=\frac{4}{4+1+25}[/tex]
[tex]\text{Probability that cup will land on its top}=\frac{4}{30}[/tex]
[tex]\text{Probability that cup will land on its top}=0.133[/tex]
[tex]\text{Probability that cup will land on its bottom}=\frac{1}{4+1+25}[/tex]
[tex]\text{Probability that cup will land on its bottom}=\frac{1}{30}[/tex]
[tex]\text{Probability that cup will land on its bottom}=0.0333[/tex]
[tex]\text{Probability that cup will land on its side}=\frac{25}{4+1+25}[/tex]
[tex]\text{Probability that cup will land on its side}=\frac{25}{30}[/tex]
[tex]\text{Probability that cup will land on its side}=0.833[/tex]
Since the outcomes of an experiment are equally likely to occur, when the probability of each outcome is equal.
We can see that probability of cup landing on its side is 0.833, which is greater than the probability of cup landing on its top (0.133) and cup landing on its bottom (0.033).
Since the probabilities of 3 outcomes are different, therefore, three outcomes of Hudson's experiment are not equally likely to occur.
