Question

You spin the spinner below one time.What is the probability of spinning anumber less than 5? Write youranswer as a percent.2 516105339

Answer 1

Hello there. To solve this question, we have to remember some properties about probabilities.

Given the following spinner:

We want to determine the probability of spinning a number less than 5.

For this, think of the numbers in the spinner as the following set:

`\{0,0,1,1,2,3,4,5,5,6\}`

We have 10 numbers and this is the size of the sample we're working with.

Now, we need to find the probability of spinning a number less than 5.

We can do this directly or using the complimentary event:

`\begin{gathered} P(n<5)+P(n\geq5)=1 \\ \\ \Rightarrow P(n<5)=1-P(n\geq5) \end{gathered}`

In this case, the probability of spinning a number that is greater than or equal to 5 is the complimentary probability of the one we want to determine and it is easier:

Notice we only have 3 numbers that are greater than or equal to 5: 5, 5 and 6.

Therefore, the probability is calculated as the ratio between the number of favorable events to an event E happening (3) and the size of the sample, 10.

In this case, we get

`P(n<5)=1-(3)/(10)`

Adding the fractions, we get

`P(n<5)=(7)/(10)`

Which is written in percent as

`P(n<5)=0.7`