Question

Jessica wants to make a spinner that has all of the following characteristicsSketch a possible spinner for Jessica. Be sure to label each section of thespinner with a name and with its theoretical probability.• Blue, red, purple, and green are the only colors on the spinner.• It is half as likely to land on blue as to land on red.• It is three times as likely to land on purple as green.• There is a 50% probability of landing on either blue or red and a 50%probability of landing on either purple or green.

Answer 1

First we have to split the spinner into two equal parts. One half belongs to the blue and red sections, and the other half belongs to the green and purple sections.

Formulating an equation for the first part, we have:

P(b) + P(r) = 0.5 ( P(b): probability of landing on blue section, P (r): probability of landing on red section)

P(r) + 1/2*P(r) = 0.5 ( Since it is half as likely to land on blue as to land on red)

3/2*P(r) = 0.5 (Adding like terms)

P(r)= 0.5 / (3/2) (Dividing on both sides by 3/2)

P(r)= 1/3 (Dividing)

P(b)=1/2*P(r) (Finding the probability of landing on blue section)

P(b)= 1/6

Formulating an equation for the second part, we have:

P(g) + P(p) = 0.5 ( P(g): probability of landing on green section, P (r): probability of landing on purple

section)

P(g) + 3*P(g) = 0.5 ( Since it is three times as likely to land on purple as green)

4*P(g) = 0.5 ( Adding like terms)

P(g) = 0.5/4 (Dividing by 4 on both sides of the equation)

P(g) = 1/8 (Dividing)

P(p) = 3*P(g) (Finding the probability of landing on purple section)

P(p)= 3/8