A spinner is broken up into three colors. The results of spinning it 20 times are given below. Fine the theoretical probability of…
1. Spinning red
2.Spinning green
3.Spinning blue
4.Spinning red or blue
To find the theoretical probability of each event, we need to count the number of favorable outcomes and divide it by the total number of possible outcomes.
To begin, let's examine the given data for the 20 spins:
1. Number of spins resulting in red: 9
2. Number of spins resulting in green: 7
3. Number of spins resulting in blue: 4
Now, let's calculate the theoretical probability for each event:
1. Theoretical probability of spinning red:
Total number of spins resulting in red = 9
Total number of spins = 20
Probability of spinning red = Number of spins resulting in red / Total number of spins = 9 / 20 = 0.45 or 45%
2. Theoretical probability of spinning green:
Total number of spins resulting in green = 7
Total number of spins = 20
Probability of spinning green = Number of spins resulting in green / Total number of spins = 7 / 20 = 0.35 or 35%
3. Theoretical probability of spinning blue:
Total number of spins resulting in blue = 4
Total number of spins = 20
Probability of spinning blue = Number of spins resulting in blue / Total number of spins = 4 / 20 = 0.2 or 20%
4. Theoretical probability of spinning red or blue:
To find this probability, we sum up the number of spins resulting in red and the number of spins resulting in blue and divide it by the total number of spins. In this case:
Total number of spins resulting in red or blue = Number of spins resulting in red + Number of spins resulting in blue = 9 + 4 = 13
Total number of spins = 20
Probability of spinning red or blue = Number of spins resulting in red or blue / Total number of spins = 13 / 20 = 0.65 or 65%
Therefore, the theoretical probability for each event is as follows:
1. Theoretical probability of spinning red: 0.45 or 45%
2. Theoretical probability of spinning green: 0.35 or 35%
3. Theoretical probability of spinning blue: 0.2 or 20%
4. Theoretical probability of spinning red or blue: 0.65 or 65%