Question

the probability that a professional baseball player will get a hit is 1/3. calculate the exact probability that he will get at least 3 hits in 5 attempts

Answer 1

The Binomial Distribution applies:
\[P(X=x)=\left(\begin{matrix}n \\ x\end{matrix}\right)\pi ^{2}(1-\pi)^{n-x}\]where there are n trials with a probability 'pi' of success on each trial and P(X = x) is the probability of exactly x successes. Substituting the given values in the above equation:\[P(X=3)=\frac{5\times4}{2}\times (\frac{1}{3})^{3}\times (\frac{2}{3})^{2}\]
Can you calculate the answer?