Question

It is equally probable that the pointer on the spinner shown will land on any one of 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 5.

Answer 1

Answer:

Probability that the pointer will stop on an odd number or a number greater than 5 is 0.75.

Step-by-step explanation:

We are given that it is equally probable that the pointer on the spinner shown will land on any one of eight regions, numbered 1 through 8.

And we have to find the probability that the pointer will stop on an odd number or a number greater than 5.

Let the Probability that pointer will stop on an odd number = P(A)

Probability that pointer will stop on a number greater than 5 = P(B)

Probability that pointer will stop on an odd number and on a number greater than 5 =  $P(A\bigcap B)$

Probability that pointer will stop on an odd number or on a number greater than 5 =  $P(A\bigcup B)$

Here, Odd numbers = {1, 3, 5, 7} = 4

Numbers greater than 5 = {6, 7, 8} = 3

Also, Number which is odd and also greater than 5 = {7} = 1

Total numbers = 8

Now, Probability that pointer will stop on an odd number =  $\frac{4}{8}$  = 0.5

Probability that pointer will stop on a number greater than 5 =  $\frac{3}{8}$  = 0.375

Probability that pointer will stop on an odd number and on a number greater than 5 =  $\frac{1}{8}$  = 0.125

Now,    $P(A\bigcup B) = P(A) +P(B) -P(A\bigcap B)$

                            =  0.5 + 0.375 - 0.125

                            =  0.75

Hence, probability that the pointer will stop on an odd number or a number greater than 5 is 0.75.