During an experiment a coin is flipped 30 times. The number of times the coin landed on heads was 18, and tails was 12. What is the experimental probability of heads or tails?

Answer 1

Pr(H) = 18/30 = 3/5 = .6 = 60% chance of heads

Pr(T) = 12/30 = 2/5 = .4 = 40% chance of tails

that's the "experimental probability" assuming the coin is not fair.

IF it's a fair coin, the probability remains 50% for heads or tails, regardless of the experimental results

n=30, p=.6 q= .4

Expected value = mean = 30(.6) = 18 heads with 30 flips

variance = npq = 18(.4) = 7.2

Null hypothesis is p=q=.5

mean = 30(.5) = 15

variance = 15(.5) = 7.5

standard deviation = sqr7.5 = about 2.7

With 10% margin of error, 18 is within less than 2 standard deviations from the mean so fail to reject the null hypothesis that the coin is fair.

Traditional statistics is all or nothing. reject a null hypothesis or fail to reject it. Based on induction.

Bayesian Statistics is deductive, a middle way between reject or not reject, just adjust the null hypothesis based on new evidence

Pr(H/E)Pr(E) = Pr(E/H)P(H)

where H is the null hypothesis and E is the evidence

Pr(H/E) = post posterior probability of a fair coin given 18 of 30 heads

Pr(E) = a priori Probability of 18 of 30 heads

Pr(E/H) = post posterior Probability of 18 of 30 heads if it's a fair coin

Pr(H) = Probability it's a fair coin, a prior probability = 1

solve for Pr(H/E) and get between 50% chance and 60%. the evidence suggests an upward revision in the hypothesis but not so much as a full scale rejection of 50%