use for 7 - 9: the wheel below is spun. find each probability. 7. p(black | a) 8. p(c | white) 9. p(black |…

Explanation:

Step1: Recall conditional - probability formula

$P(A|B)=\frac{P(A\cap B)}{P(B)}$

Step2: Analyze question 7

1. First, find the number of sections labeled 'A'. There are 3 sections labeled 'A'.
2. Then, find the number of sections that are both black and labeled 'A'. There is 1 section that is black and labeled 'A'.
3. Calculate $P(\text{black}|\text{A})$ using the formula: $P(\text{black}|\text{A})=\frac{n(\text{black}\cap\text{A})}{n(\text{A})}=\frac{1}{3}$

Step3: Analyze question 8

1. Find the number of white - colored sections. There are 5 white - colored sections.
2. Find the number of sections that are both white and labeled 'C'. There is 1 section that is white and labeled 'C'.
3. Calculate $P(\text{C}|\text{white})$ using the formula: $P(\text{C}|\text{white})=\frac{n(\text{C}\cap\text{white})}{n(\text{white})}=\frac{1}{5}$

Step4: Analyze question 9

1. Find the number of sections labeled 'B' or 'E'. There are 3 sections labeled 'B' and 2 sections labeled 'E', so $n(\text{B or E}) = 3 + 2=5$.
2. Find the number of sections that are both black and labeled 'B' or 'E'. There are 2 sections that are black and labeled 'B' or 'E' (1 black 'B' and 1 black 'E').
3. Calculate $P(\text{black}|\text{B or E})$ using the formula: $P(\text{black}|\text{B or E})=\frac{n(\text{black}\cap(\text{B or E}))}{n(\text{B or E})}=\frac{2}{5}$

Answer:

7. $\frac{1}{3}$
8. $\frac{1}{5}$
9. $\frac{2}{5}$