Exercise 84 Page 513

To find the expected number of times the spinner ends up in each region, we first have to calculate the probability of spinning the regions. This is the ratio of the region's central angle to 360^(∘). We know the central angle of A and B, so we can write an equation to find the central angle of C. m∠ C+135^(∘)+90^(∘) =180^(∘) ⇔ m∠ C = 135^(∘)With this information, we can calculate the probability of spinning each region.

When we know the probability of spinning A, B and C, we can calculate the expected number of times we will spin each region by multiplying the number of spins by the corresponding probability. A: 1/4(80)=20 [0.7em] B: 3/8(80)=30 [0.7em] C: 3/8(80)=30