1. in a particular game, a spinner with four equally-sized sectors labeled 1, 3, 5, and 6 is spun twice. one turn is considered 2 spins of the spinner.

if the sum of the spins is even, you move backward 6 spaces. otherwise, you move forward 2 spaces.

what is the mathematical expectation for the number of spaces moved in one turn?
3 spaces forward

1 space backward

3 spaces backward

1 space forward


2. anya may choose one of two options for the method in which she may be awarded a money prize.

option a: spin a spinner twice. the spinner is divided into four equally-sized sectors numbered 1, 2, 5, and 5. if the sum of the two spins is greater than 6, anya is awarded $8. otherwise, she must pay $2.

option b: flip a coin three times. if heads appear 3 times, anya is awarded $50. otherwise, she must pay $1.

anya chooses the option with the greater mathematical expectation.

how much more money can anya expect to make by choosing this option over the other option?