A pupil conducting a coin tossing experiment was surprised when she dropped 20 coins on to the floor and obtained only 5 heads.
Calculate using an appropriate binomial distribution the probability that 20 fair coins dropped onto the floor at random will show exactly 5 heads.
My attempt,
$$\begin{align}\Pr(X{=}5) &={^{20}{\sf C}_5}(0.25)^5(0.75)^{15} \\[1ex] & =0.2023\end{align}$$
But the answer given is $0.0148$. Why?
I'm not sure why you used the number of heads from the sample drops to calculate the probability, but you are dropping a fair coin. Thus the probability of heads is $0.5$, as is tails. Hence your probability is given by $$ {20 \choose 5} (0.5)^{5}(0.5)^{15} $$