Question

You flip a coin 200 times and it lands heads up every time what is the approximate probadilaty

Answer 1

Assume the coin is fair.

As a result, the probability of it being heads one time is 1/2. Now when you flip the coin a second time, what happened on the 1st flip won't affect the 2nd flip. We say these are independent events because what happened the 1st time won't affect the second one. When two events are independent, their probabilites is the product of them.

So the probability of two heads is 1/2 * 1/2 = 1/4.

Now we repeat it for three times. Again, each of the three flips won't affect for the other.

The probability of three heads is 1/2 * 1/2 * 1/2 = 1/8.

Notice a pattern developing.

P(one head) = 1/2¹ = 1/2

P(two heads) = 1/2² = 1/4

P(three heads) = 1/2³ = 1/8

The exponent refers to the amount of times the coin is flipped. So, the probability of 200 heads is $\frac{1}{2^{200}}$.