if you flip three fair coins, what is the probability that the first two flips will both be heads, and the…
if you flip three fair coins, what is the probability that the first two flips will both be heads, and the third flip will be either heads or tails?
Answer
Explanation:
Step1: Calculate probability of first - head
The probability of getting a head in a single fair - coin flip is $\frac{1}{2}$.
Step2: Calculate probability of second - head
Since coin flips are independent events, the probability of getting a head on the second flip is also $\frac{1}{2}$.
Step3: Calculate probability of third - head or tail
The probability of getting a head or a tail on the third flip is 1 (because it's certain that we'll get either a head or a tail).
Step4: Calculate combined probability
Using the multiplication rule for independent events, the combined probability $P$ is $P=\frac{1}{2}\times\frac{1}{2}\times1$. $P = \frac{1}{4}$
Answer:
$\frac{1}{4}$