The experiment was carried out 100 times times and it was noted that three heads occurred 40 times. What is the difference between the experiment probability of getting three heads and its theoretical probability.
Theoretical probability of getting three heads in a row is given by:
P(3 heads) = (1/2)^3 = 1/8
Experimental probability of getting three heads in a row is given by:
P(experimental) = 40/100 = 0.4
The difference between the two probabilities is:
0.4 - 1/8 = 0.375
Therefore, the difference between the experiment probability of getting three heads and its theoretical probability is 0.375 or 37.5%.
To find the difference between the experimental probability and the theoretical probability of getting three heads, we first need to calculate each probability.
Theoretical Probability:
The theoretical probability of getting three heads in a row when flipping a fair coin is given by the formula:
P(3 heads) = (P(Head))^3
Since a fair coin has a 50% chance of landing on heads, we can substitute this value into the formula:
P(3 heads) = (0.5)^3 = 0.125 = 12.5%
Experimental Probability:
The experimental probability is the actual observed probability based on the data from the 100 trials. In this case, we observed three heads occurring 40 times out of 100 trials.
Experimental Probability = Number of successful outcomes / Total number of trials
P(3 heads) = 40/100 = 0.4 = 40%
Difference:
To find the difference between the experimental probability and the theoretical probability, we subtract the theoretical probability from the experimental probability:
Difference = Experimental Probability - Theoretical Probability
Difference = 40% - 12.5% = 27.5%
Therefore, the difference between the experimental probability of getting three heads and its theoretical probability is 27.5%.