A spinner is divided into 6 equal sections and colored as shown. The spinner is spun 60 times, and the results are recorded in the table.
A spinner with 6 equal sections. 3 sections are Red. 2 sections are Yellow. 1 section is Blue.
Red Blue Yellow
24 14 22
Question
Move symbols into the blanks to correctly complete the inequalities comparing the experimental probability and theoretical probability for each color.
Response area with 3 blank spaces
Experimental P (Red)
Blank space 4 empty
Theoretical P (Red)
Experimental P (Blue)
Blank space 5 empty
Theoretical P (Blue)
Experimental P (Yellow)
Blank space 6 empty
Theoretical P (Yellow)
Answer options with 3 options.
Experimental P (Red) = 0.4
Blank space 4 = < (less than)
Theoretical P (Red) = 0.5
Experimental P (Blue) = 0.233
Blank space 5 = >
Theoretical P (Blue) = 0.1667
Experimental P (Yellow) = 0.367
Blank space 6 = ≈ (approximately equal to)
Theoretical P (Yellow) = 0.3333
Experimental P (Red) is 24/60 or 2/5.
Theoretical P (Red) is 3/6 or 1/2.
Experimental P (Blue) is 14/60 or 7/30.
Theoretical P (Blue) is 1/6 or 5/30.
Experimental P (Yellow) is 22/60 or 11/30.
Theoretical P (Yellow) is 2/6 or 1/3.
To complete the inequalities comparing the experimental probability and theoretical probability for each color, we first need to calculate the experimental and theoretical probabilities for each color.
Experimental probability is the ratio of the number of times an event occurs to the total number of trials. In this case, the event is landing on a specific color, and the total number of trials is 60.
Theoretical probability is the expected probability of an event occurring based on the underlying probability distribution. In this case, we can determine the theoretical probability by dividing the number of sections of a specific color by the total number of sections on the spinner.
Let's calculate the probabilities for each color:
Experimental P (Red) = Number of times Red occurred / Total number of trials
Experimental P (Red) = 24 / 60
Experimental P (Red) = 0.4 or 2/5
Theoretical P (Red) = Number of Red sections / Total number of sections
Theoretical P (Red) = 3 / 6
Theoretical P (Red) = 0.5 or 1/2
Experimental P (Blue) = Number of times Blue occurred / Total number of trials
Experimental P (Blue) = 14 / 60
Experimental P (Blue) = 0.2333 ≈ 0.23 or 14/60 ≈ 7/30
Theoretical P (Blue) = Number of Blue sections / Total number of sections
Theoretical P (Blue) = 1 / 6
Theoretical P (Blue) = 0.1667 ≈ 0.17 or 1/6
Experimental P (Yellow) = Number of times Yellow occurred / Total number of trials
Experimental P (Yellow) = 22 / 60
Experimental P (Yellow) = 0.3667 ≈ 0.37 or 22/60 ≈ 11/30
Theoretical P (Yellow) = Number of Yellow sections / Total number of sections
Theoretical P (Yellow) = 2 / 6
Theoretical P (Yellow) = 0.3333 ≈ 0.33 or 1/3
Now, let's fill in the blanks with the correct inequalities:
Experimental P (Red) < Theoretical P (Red)
0.4 < 0.5 or 2/5 < 1/2
Experimental P (Blue) < Theoretical P (Blue)
0.23 < 0.17 or 14/60 < 1/6
Experimental P (Yellow) > Theoretical P (Yellow)
0.37 > 0.33 or 22/60 > 1/3
So the completed inequalities are:
Experimental P (Red) < Theoretical P (Red)
Experimental P (Blue) < Theoretical P (Blue)
Experimental P (Yellow) > Theoretical P (Yellow)