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

The probability that the spinners land on colors summing up to exactly 3 is 1/8, considering there are two combinations that give us a sum of 3 and a total of 16 possible outcomes.

Step-by-step explanation:

To calculate the probability of the spinners landing on colors that sum to exactly 3, we need to consider the different color combinations that lead to this sum. The combinations that give us a sum of 3 are red (1) + blue (2) and yellow (2) + red (1). Since each spinner has four colors, there are a total of 4 x 4 = 16 possible outcomes when spinning both spinners. The combination red + blue can occur in two different ways: red on the first spinner and blue on the second, or blue on the first spinner and red on the second. Therefore, 2 outcomes give us a sum of 3. The probability of getting a sum of 3 is then 2/16, which simplifies to 1/8. Therefore, the probability that the spinners land on colors summing up to exactly 3 is 1/8.

Answer 2

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=(2)/(16)=(1)/(8)=0.125.`

Answer:
`Pr=(1)/(8)=0.125.`