If you randomly pick a coin from a box that contains $90\%$ fair coins and $10\%$ loaded coins, (a loaded coin gives heads $90\%$ of the time), toss it $5$ times and get all heads. What is the probability that this is a loaded coin?
$$n = 5, x = 5, p = 0.1(0.9)^5$$
Where $n$ is the number of flips, $x$ is number of heads, and $p$ is the probability of getting heads. so $$( 0.1 (0.9)^5 ) + (0.9 (0.5)^5) = 0.087$$
Can anyone see if the answer I provided is correct or not !