Question

At a casino, a combination of two spinners is used to decide the winner based on the sum of scores from spinning. the spinners each have four colored spaces - red, yellow, blue, and green. red = 1, yellow = 2, blue = 3, and green = 4 what is the probability that the spinners land on colors summing up to exactly 3?

Answer 1

Consider the table

$\begin{array}{ccccc}\text{Spinners} & 1 & 2 & 3 & 4 \\1 & 1+1 & 1+2 & 1+3 & 1+4 \\2 & 2+1 & 2+2 & 2+3 & 2+4 \\3 & 3+1 & 3+2 & 3+3 & 3+4 \\4 & 4+1 & 4+2 & 4+3 & 4+4\end{array}$

In this table are given all 16 possible outcomes of spinning two spinners. In rows the first number is the number that was spinned on 1st spinner and the second number is the number that was spinned on 2nd spinner. As you can see only 2 of them are those that give 3 in sum (1+2 and 2+1). Then the probability that the spinners land on colors summing up to exactly 3 is

$Pr=\dfrac{2}{16}=\dfrac{1}{8}=0.125.$

Answer: $Pr=\dfrac{1}{8}=0.125.$