Question

What is the probability of flipping a coin and it coming up heads four times in a row

Answer 1

In a single toss, the probability that the result of the toss is head is 1/2:
$P_1 (head) = \frac{1}{2}$

For 2 tosses in a row, the probability that the result is head in both tosses is
$P_2 = P_1 \cdot P_1 = ( \frac{1}{2} )( \frac{1}{2} )= \frac{1}{4}$

If we continue, we find that the probability to have 4 heads in 4 consecutive tosses is given by
$P_4 = ( P_1 (head) )^4 = ( \frac{1}{2} )^4 = \frac{1}{16}$