Question

In a of chance, players spin a pointer on a spinner with eight equal sized sections. Part A what is the same space of this?A. {1,12,3,4,4,5,5}B. {1,2,2,2,3,3,4,5}C.{1,2,2,3,3,4,5,5}D.{1,1,2,3,3,4,5,5}Part BWhat are the probabilities of each outcome in the sample space.

Answer 1

ANSWER

PART A: D. {1, 1, 2, 3, 3, 4, 5, 5}

PART B:

• P(1) = 1/4

,

• P(2) = 1/8

,

• P(3) = 1/4

,

• P(4) = 1/8

,

• P(5) = 1/4

EXPLANATION

PART A

The sample space is a list - if it is discrete - of all the posible outcomes of the experiment.

In this spinner there are two number 1, one number 2, two number 3, one number 4 and two number 5. Therefore the sample space is {1, 1, 2, 3, 3, 4, 5, 5}

PART B

Note that though the spinner is divided into 8 equal spaces the number of posible outcomes is 5, because some of the numbers are repeated.

Each item in the sample space is equally likely to come up: the probability of each item is 1/8 (one out of 8 outcomes) but each number has different probabilities:

We have two 1s, so the probability is twice the probability of one:

$P(1)=\frac{2}{8}=\frac{1}{4}$

There is only one 2, so the probability is:

$P(2)=\frac{1}{8}$

In the same way, we have two 3s and two 5s:

$\begin{gathered} P(3)=\frac{2}{8}=\frac{1}{4} \\ P(5)=\frac{2}{8}=\frac{1}{4} \end{gathered}$

And there's one 4:

$P(4)=\frac{1}{8}$