A person playing a game of chance has a 0.25 probability of winning. If the person plays the game 20 times and wins half of that number of times, what is the difference between the theoretical probability and the experimental probability of that person winning ?
0.50
0.25
0.30
0.75
The theoretical probability of winning is calculated by finding the ratio of the number of favorable outcomes to the total number of possible outcomes. In this case, the person has a 0.25 probability of winning, so the theoretical probability is 0.25.
The experimental probability of winning is calculated by finding the ratio of the number of times the person actually wins to the total number of times they played the game. In this case, the person played the game 20 times and won half of that number, which is 10.
So, the experimental probability of winning is 10/20 = 0.50.
The difference between the theoretical probability and the experimental probability is the absolute value of the difference between these two values. In this case, the difference is:
|0.25 - 0.50| = 0.25
Therefore, the difference between the theoretical probability and the experimental probability of that person winning is 0.25.
To find the difference between the theoretical probability and the experimental probability, we first need to calculate both probabilities.
The theoretical probability is the probability of an event occurring based on logic and reasoning. In this case, the person has a 0.25 probability of winning each time they play the game. If they play the game 20 times, the theoretical probability of winning is (0.25 * 20) = 5.
The experimental probability is the probability of an event occurring based on actual observations or data. In this case, the person wins half of the number of times they played the game, which is (20 / 2) = 10.
Now, to find the difference between the theoretical probability and the experimental probability, we subtract the experimental probability from the theoretical probability:
Difference = Theoretical Probability - Experimental Probability
Difference = 5 - 10
Difference = -5
Therefore, the difference between the theoretical probability and the experimental probability is -5.
in practice 0.5
in theory 0.25
difference = ?