Answer:
[tex]9C3*(0.5)^3(0.5)^6[/tex]
Step-by-step explanation:
The binomial probability formula shown has variables which represents:
n is the total number of trials (here, we flip penny 9 times, hence n = 9)
k is the number we want to find (here, we want the probability of 3 heads, so k = 3)
p is the probability of success (here, success means getting heads. So, in a coin flip the probability of heads is always 1/2, so p = 1/2)
Putting all the info into the equation and using formula for nCk, we get:
[tex]P(k successes)=nCk*p^{k}(1-p)^{n-k}\\P(3Heads)=9C3*(0.5)^3(1-0.5)^{9-3}\\P(3Heads)=9C3*(0.5)^3(0.5)^6[/tex]
The first expression shown in the answer choices is right.
