I am reading "Schaum's Outline of Statistics". I understand the examples in the book, and as a result, I have produced my own probability question, but I am having difficulty in attempting to solve it.
Using Binomial Distribution:
A fair six-sided die is rolled once.
Calculate the probability of getting either a $1$ or a $4$.
This is what I have attempted:
$Success(P) = 2/6 = 0.\dot3$
$Failure(Q) = 4/6 = 0.\dot6$
$= (^1C_3) (0.\dot3)^1 (0.\dot6)^1-1$
$= 0.3\dot2$
This obviously is not correct. I am attempting to solve this question using Binomial Distribution. What am I doing incorrectly?
Using the binomial formula you still get the same answer:
You need $1$ success out of $1$ try, so:
$$P = {1 \choose 1} \cdot P(Success)^1 \cdot P(Failure)^0 = 1 \cdot \big(\frac{2}{6}\big)^1 \cdot \big(\frac{4}{6}\big)^0 = 1 \cdot \frac{2}{6} \cdot 1 = \frac{2}{6}$$