(Solved): P(x)=nCxpxqnx=(nx)!x!n!pxqnx 1. Find Binomial Probability by using Formula Rotato ...

$P(x)={}_n{C}_x{p}^x{q}^{n?x}=\frac{n!}{(n?x)!x!}{p}^x{q}^{n?x}$ 1. Find Binomial Probability by using Formula Rotator cuff surgery has a $80\%$ chance of success. The surgery is performed on four patients. Find the probability of the surgery being successful on exactly two patients. (Source: The Orthopedic Center of St. Louis) 2. Finding Binomial Probabilities Using Formulas $P(x)={}_n{C}_x{p}^x{q}^{n?x}=\frac{n!}{(n?x)!x!}{p}^x{q}^{n?x}$ A survey found that $22\%$ of U.S. adults say that the economy, unemployment, and jobs are the most important problems facing the U.S. today. You randomly select four adults and ask them whether the economy, unemployment, and jobs are the most important problems facing the U.S. today. Find the probability that (1) exactly two of them respond yes, (2) at least two of them respond yes, and (3) fewer than two of them respond yes. (Source: Ipsos)