Part (a)
- Theoretical = 1/4
- Experimental = 3/10
- Comparison: The experimental probability is larger
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How to get those answers:
To get the theoretical probability of landing on A, we count out the number of spaces labeled "A". There are 3 such spaces. This is out of 12 spaces total (it might help to break it up into quarters, then each quarter is cut into 3 equal pieces to get 4*3 = 12 pieces total).
The theoretical probability of landing on A is 3/12 = 1/4
The experimental or empirical probability is where we divide what is shown in the frequency table. The "A" shows up 18 times out of 60, so we get 18/60 = (6*3)/(6*10) = 3/10
Looking at the decimal form of each value, we have
1/4 = 0.25
3/10 = 0.30
We see that the experimental probability 3/10 is larger
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Part (b)
- Theoretical = 3/4
- Experimental = 7/10
- Comparison: Theoretical probability is larger
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How to get those answers:
From the previous part, we found that 1/4 is the chances of landing on A. So 3/4 is the chances of not landing on A. The two fractions add to 1 to represent 100% of the situations possible. Either you land on A, or you don't. Or notice how 1 - (1/4) = 3/4.
We use the same idea for the experimental probability
1 - (3/10) = 10/10 - 3/10 = 7/10
The experimental probability of not landing on A is 7/10.
Now find the decimal form of each fraction.
3/4 = 0.75
7/10 = 0.70
This time the theoretical probability 3/4 is larger
The reason the theoretical and experimental probabilities aren't exactly the same is due to random chance. The more times you spin the spinner, say 1000s of times, then the experimental probability should get closer to the theoretical one. The theoretical probabilities will stay the same no matter how many spins you do.