To design a spinner with the given probabilities, we can use the following sectors:
A sector covering 60 degrees for the number 1, with probability 1/6.
A sector covering 120 degrees for the number 3, with probability 1/3.
A sector covering 180 degrees for the number 7, with probability 1/2.
A sector covering 180 degrees for the odd numbers (1 and 3), with probability 1.
To create the spinner, draw a circle and divide it into four equal sectors. Color one sector red for the number 1, color two adjacent sectors green for the number 3, color one remaining sector blue for the number 7. Finally, color half of the blue sector green to represent the odd numbers.
The resulting spinner will have the desired probabilities: P(1) = 1/6, P(3) = 1/3, P(7) = 1/2, P(odd number) = 1.