Question

Which is more likely? Flipping a coin 10 times and getting more than 70% heads or flipping a coin 50 times and getting more than 70% heads? Explain in as much detail as you can.

Answer 1

For n = 10

p = 0.5

It is a binomial distribution.

P(X > 7) = P(X = 8) + P(X = 9) + P(X = 10)

             = 10C8 * (0.5)^8 * (0.5)^2 + 10C9 * (0.5)^9 * (0.5)^1 + 10C10 * (0.5)^10 * (0.5)^0 = 0.0547

For n = 50

       p = 0.5

= n * P = 50 * 0.5 = 25

= sqrt(np(1 - p))

= sqrt(50 * 0.5 * 0.5) = 3.5355

P(X > 35)

= P(X > 35.5)

= P((X - )/> (35.5 - )/)

= P(Z > (35.5 - 25)/3.5355)

= P(Z > 2.97)

= 1 - P(Z < 2.97)

= 1 - 0.9985

= 0.0015

Since the probability value for n = 10 trials is more than n = 50 trials , so flipping a coin of 10 times is more likely.