The experiment involved tossing a coin simultaneously. The experiment was carried out 100 times, and it was noted that three heads occurred 40 times. What is the difference between the experimental probability of getting three heads and its theoretical probability? Write the answer in the simplest form of fraction.
The theoretical probability of getting three heads when tossing a coin simultaneously is calculated using the binomial probability formula:
P(x) = nCx * p^x * (1-p)^(n-x)
Where:
n = total number of trials = 100
x = number of successful outcomes (in this case, 3 heads)
p = probability of success on a single trial = 0.5 for a fair coin
So, the theoretical probability is:
P(3 heads) = 100C3 * 0.5^3 * (1-0.5)^(100-3)
= 161700 * 0.125 * 0.5^97
= 161700 * 0.125 * (1/2)^97
= 161700 * 0.125 * (1/(2^97))
= 161700 * 0.125 * (1/2^97)
= 161700 * 0.125 * (1/2^97)
= 161700 * 0.125 * (1/2^97)
= 161700 * 0.125 * (1/2^97)
= 161700 * 0.125 * (1/2^97)
= 161700 * 0.125 * (1/2^97)
= 8095/2^97
Now, the experimental probability of getting three heads is the number of times it occurred divided by the total number of trials:
Experimental Probability = 40/100 = 2/5
Therefore, the difference between the experimental and theoretical probabilities is:
Difference = Experimental Probability - Theoretical Probability
Difference = 2/5 - 8095/2^97
Simplify the fractions to get the final answer.