Question

what is the probability of tossing a coin and getting a head 4 times in a row?
a. $\frac{1}{2}$
b. $\frac{1}{4}$
c. $\frac{1}{8}$
d. $\frac{1}{16}$
e. $\frac{1}{24}$

Explanation:

Step1: Determine single - toss probability

The probability of getting a head in a single coin - toss is $P(H)=\frac{1}{2}$, since a coin has 2 equally likely outcomes (head or tail).

Step2: Use multiplication rule for independent events

Since coin - tosses are independent events, the probability of getting a head 4 times in a row is $P = P(H)\times P(H)\times P(H)\times P(H)$.
Substitute $P(H)=\frac{1}{2}$ into the formula: $P=\frac{1}{2}\times\frac{1}{2}\times\frac{1}{2}\times\frac{1}{2}=\frac{1}{16}$.

Answer:

D. $\frac{1}{16}$