The results of rolling a 6-sided die 120 times are given in the table. use the table to find the experimental and probability of each event. then find the theoretical probability of each event.

According to the results of rolling a 6-sided die 120 times, we have:

Rolling a 2:

Experimental = 15/120 = 1/8 = 0.125 = 12.5%

Theoretical = 20/120 = 1/6 = 0.1667 = 16.67%

Rolling a 1:

Experimental = 18/120 = 3/20 = 0.15 = 15%

Theoretical = 20/120 = 1/6 = 0.1667 = 16.67%

Rolling a 1 or 6:

Experimental = 18/120 + 20/120 = 38/120 = 19/60= 0.3167 = 31.67%

Theoretical = 20/120 + 20/120 = 40/120 = 1/3 = 0.3333 = 33.33%

Step-by-step explanation:

1. First of all, let's recall what is the difference between experimental and theoretical probability of an event.

The experimental probability is the result of an experiment, and the theoretical probability is based on the mathematical model developed in the theory of probability.  In simple words, the most important difference is that the experimental probability is based on what actually happens and the theoretical probability on what is expected to happen.

The accuracy of the results of the experiments depends directly on the sample size of the experiment and the accuracy is greater when the sample size is larger.

For this particular event the theoretical probability is the same for rolling each number of the die, 1/6 or 16.67%

Now, let's complete the answer this way:

Rolling a 2:

Experimental = 15/120 = 1/8 = 0.125 = 12.5%

Theoretical = 20/120 = 1/6 = 0.1667 = 16.67%

Rolling a 1:

Experimental = 18/120 = 3/20 = 0.15 = 15%

Theoretical = 20/120 = 1/6 = 0.1667 = 16.67%

Rolling a 1 or 6:

Experimental = 18/120 + 20/120 = 38/120 = 19/60= 0.3167 = 31.67%

Theoretical = 20/120 + 20/120 = 40/120 = 1/3 = 0.3333 = 33.33%

x² + 11x + 18 < 0  

[-11 ± sqrt(121 - 72)]/2 = (-11 ± 7)/2  

solution: (-9, -2)

step-by-step explanation:

substitute,

circle 1 = 5

circle 2 = 20

circle 3 = 44

in this case no matter how you add, you will always get a perfect square..

hence proved

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