Question

Suppose you have a random spinner with sides labeled with the numbers 1, 2, 3, and 4. You spin it once, record the number, and spin it again. Let X be the sum of the two numbers the spinner lands on. Find the probability of X<5.

Answer 1

Let's take a look first at the possible outcome of the spinner which will determine our sample size. Since we have four different numbers that can be combined with the same number set, we are arriving at a sample size equal to 16. The following events will happen upon spinning the random spinner twice,

`\begin{gathered} (1,1),(1,2),(1,3),(1,4) \\ (2,1),(2,2),(2,3),(2,4) \\ (3,1),(3,2),(3,3),(3,4) \\ (4,1),(4,2),(4,3),(4,4) \end{gathered}`

Among all of these combinations, the combinations that have a sum of less than 5 are

`(1,1),(1,2),(1,3),(2,1),(2,2),(3,1)`

We have 6 samples that can have a sum of less than 5 out of 16 possible outcomes. Hence, the probability can be computed as

`P=(6)/(16)=(3)/(8)=0.375`

The probability that the spinner will land at a combination that is less than 5 is 0.375 or 37.5%.

Answer: 0.375 or 37.5%