Question

In a factory, a species of oranges have a 1/3 chance of having a pit. What is the probability that, at most, 1 out of 4 oranges have a pit?

Answer 1

Do you know the binomial distribution?

Answer 2

Nope.

Answer 3

\[P(0\ with\ pit)=\left(\begin{matrix}4 \\ 0\end{matrix}\right)(\frac{1}{3})^{0}(1-\frac{1}{3})^{4}=(\frac{2}{3})^{4}\]
\[P(1\ with\ pit)=\left(\begin{matrix}4 \\ 1\end{matrix}\right)(\frac{1}{3})^{1}(1-\frac{1}{3})^{3}=4\times\frac{1}{3}\times (\frac{2}{3})^{3}\]
After you calculate the above 2 values of probability then add them to find the probability that at most 1 out of 4 oranges will have a pit.