Answer: 24.7%
Step-by-step explanation:
To find the probability of this compound event, we will first find the probability of each individual event.
[tex]\displaystyle \text{P(odd number)}=\frac{\text{wanted outcome}}{\text{possible outcomes}}=\frac{\text{odd number}}{\text{parts of the spinner}}=\frac{5}{9} }[/tex]
[tex]\displaystyle \text{P(not flipping heads)}=\frac{\text{wanted outcome}}{\text{possible outcomes}}=\frac{\text{flipping tails}}{\text{two sides to the coin}}=\frac{1}{2} }[/tex]
[tex]\displaystyle \text{P(not spinning a six)}=\frac{\text{wanted outcome}}{\text{possible outcomes}}=\frac{\text{1, 2, 3, 4, 5, 7, 8, 9}}{\text{parts of the spinner}}=\frac{8}{9} }[/tex]
Next, we will multiply all of these event probabilities together to find the compound event.
[tex]\displaystyle \text{P(odd number, tails, not spinning a six)}=\frac{5}{9}*\frac{1}{2}*\frac{8}{9}=\frac{40}{162}=\frac{20}{81} \approx 0.24691358[/tex]
Lastly, we will take this value and multiply it by 100 to create a percentage. Then we will round to the nearest tenth.
[tex]\displaystyle \text{P(odd number, tails, not spinning a six)} \approx 0.24691358 * 100 = 24.7\%[/tex]
