Question

it is equally probable that the pointer on the spinner shown will land on any one of the eight regions, numbered 1 through 8. if the pointer lands on a borderline, spin again. find the probability that the pointer will stop on an odd number or a number greater than 3. the probability is \boxed{}. (type an integer or a fraction. simplify your answer.)

Explanation:

Step1: Determine the number of odd numbers

The odd numbers in the range \(1 - 8\) are \(1,3,5,7\). So, \(n(\text{odd})=4\).

Step2: Determine the number of numbers greater than \(3\)

The numbers greater than \(3\) in the range \(1 - 8\) are \(4,5,6,7,8\). So, \(n(\text{greater than }3)=5\).

Step3: Determine the number of numbers that are both odd and greater than \(3\)

The numbers that are both odd and greater than \(3\) are \(5,7\). So, \(n(\text{odd and greater than }3)=2\).

Step4: Use the formula for \(P(A\cup B)\)

The formula for \(P(A\cup B)=P(A)+P(B)-P(A\cap B)\). Here, \(A\) is the event of getting an odd - number and \(B\) is the event of getting a number greater than \(3\). Since \(P(A)=\frac{n(A)}{n(S)}\), \(P(B)=\frac{n(B)}{n(S)}\) and \(P(A\cap B)=\frac{n(A\cap B)}{n(S)}\) with \(n(S) = 8\) (total number of regions).
\(P(\text{odd or greater than }3)=\frac{4 + 5-2}{8}\)

Answer:

\(\frac{7}{8}\)