Question

It is equally probable that the pointer on the spinner Shown will land on any one of the eight regions number one through eight if the pointer lands on the borderline spin again. find the probability that the pointer will stop on an even number or number greater than three

Answer 1

The even numbers here are 2, 4, 6 and 8. That is 4 numbers.

The numbers greater than 3 are 4, 5, 6, 7, and 8, that is 5 numbers.

And we have a total of 8 numbers.

Let P(A) be the probability of the pointer landing on an even number

Let P(B) be the probability of the pointer landing on a number greater than 3

Let P(A or B) be the probability that the pointer stops on an even number or number greater than three

From the probability formula,

`P(\text{A or B) = P(A) + P(B) - P(A}\cap B)`
`\text{ P(A}\cap B)\text{ means probability of A and B}`

Hence

`\begin{gathered} P(A)=(4)/(8) \\ P(B)=(5)/(8) \end{gathered}`
`\begin{gathered} \text{ For P(A}\cap B)\text{ we can s}ee\text{ that betwe}en\text{ } \\ \text{the even numbers 2, 4, 6, 8 and } \\ n\text{umbers greater than 3, which are 4, 5, 6, 7, 8} \\ \text{what is common is 4, }6,\text{ 8} \\ So,\text{ } \\ \text{P(A}\cap B)=(3)/(8) \end{gathered}`

Therefore, P(A or B) becomes

`\begin{gathered} (4)/(8)+(5)/(8)-(3)/(8) \\ (4+5-3)/(8) \\ (6)/(8) \\ =(3)/(4) \end{gathered}`