10. kaycee has won a contest. to determine the amount of her prize, she must spin this spinner twice. she…

Explanation:

Step1: Create tree - diagram for part a

The first spin has 4 possible outcomes ($50, $100, $200, $1000). For each of these outcomes, the second spin also has 4 possible outcomes. So, the tree - diagram will have 4 branches for the first spin, and from each of those branches, 4 more branches for the second spin. The total number of possible outcomes is $4\times4 = 16$. The pairs of spins and their sums are: $(50,50)=100$, $(50,100)=150$, $(50,200)=250$, $(50,1000)=1050$, $(100,50)=150$, $(100,100)=200$, $(100,200)=300$, $(100,1000)=1100$, $(200,50)=250$, $(200,100)=300$, $(200,200)=400$, $(200,1000)=1200$, $(1000,50)=1050$, $(1000,100)=1100$, $(1000,200)=1200$, $(1000,1000)=2000$.

Step2: Find minimum and maximum for part b

The minimum sum is $50 + 50=100$ and the maximum sum is $1000+1000 = 2000$. The number of outcomes that are more than 100 and less than 2000 is 14 (all except $(50,50)$ and $(1000,1000)$). The probability $P=\frac{14}{16}=\frac{7}{8}$.

Step3: Find number of outcomes greater than $500$ for part c

The pairs that give a sum greater than $500$ are: $(50,1000)$, $(100,1000)$, $(200,1000)$, $(1000,50)$, $(1000,100)$, $(1000,200)$, $(1000,1000)$. There are 7 such pairs. The probability $P=\frac{7}{16}$.

Answer:

a) Tree - diagram shows 16 possible pairs of spins and their sums as described above. b) $\frac{7}{8}$ c) $\frac{7}{16}$