Question

Problem 13. A fair coin is tossed 10000 times. Find the probability that the number of tails is more or equal to 5050.

Answer 1

n = 10000

P(tail) = 0.5

$\mu$ = n * p = 10000 * 0.5 = 5000

$\sigma$ = sqrt(np(1 - p))

    = sqrt(10000 * 0.5 * 0.5)

    = 50

P(X > 5050)

= P(X > 5049.5)

= P((X - $\mu$ )/ $\sigma$ > (5049.5 - $\mu$ )/ $\sigma$ )

= P(Z > (5049.5 - 5000)/50)

= P(Z > 0.99)

= 1 - P(Z < 0.99)

= 1 - 0.8389

= 0.1611