There is a big court case, and 20% of the adult population believe the accused is innocent prior to jury selection. Assume that the 12 jurors were selected randomly and independently from the population.

- Find the probability that the jury has at least one member who believe in the accused's innocence prior to jury selection (hint: define the binomial (12,.2) random variable X to be the number of jurors believing in the accused's innocence).

- Find the probability that the jury had at least two members who believed in the accused's innocence (hint: P(X ≥ 2) = 1-P(X ≤ 1), and P(X ≤ 1) = P(X=0) + P(X=1)).

Am I correct in thinking that for the first question, you should use the command dbinom(1,12,.2)? If this is the case, do I need to use pbinom to solve the second question? The "at least" in both statements and the hint in the second question are causing me quite some confusion.

This is certainly a stupid question, but any and all help would be greatly appreciated!