Question

A biased coin is thrown 250 times.

The relative frequency of Tails is worked out after every 50 throws.
Total number of throws
50
100
150
200
Relative frequency
0.3
0.28
0.34
0.4
Which is the best estimate of the probability of Tails?
A-28
B-0.3
C-0.36
D-0.4

Answer 1

The best estimate for the probability of tails is 0.36

From the table given,

50 rolls = 0.3

100 rolls = 0.28

150 rolls = 0.34

200 rolls = 0.4

250 rolls = 0.36

According to the central limit theorem which establishes that ; As the sample size (n) increases, the distribution of the sample means approaches a normal distribution regardless of the underlying distribution of the population, as long as the population distribution has a finite variance.

This means that , the best estimate as decided from the experimental probability values would be the event with the highest number of throws . This is because the sample mean converges to the value of the population mean as the sample size increases.

Hence, the best estimate is that obtained on 250 throws, which is 0.36