Answer:
a) [tex]\frac{1}{24}[/tex] probability that the wheel stops a "lose turn" for a single spin.
b) [tex]\frac{1}{576}[/tex] probability that the wheel stops a "lose turn" for two successive spins.
c) [tex]\frac{1}{13824}[/tex] probability that the wheel stops a "lose turn" for three successive spins.
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
24 components on the wheel, one of which is "lose a turn"
This means that each time the wheel stops, there is a [tex]\frac{1}{24}[/tex] probability that it stops at lose a turn.
a.single spin
Only one spin, so:
[tex](\frac{1}{24})^1 = \frac{1}{24}[/tex]
[tex]\frac{1}{24}[/tex] probability that the wheel stops a "lose turn" for a single spin.
b.two successive spins
Two spins, so:
[tex](\frac{1}{24})^2 = \frac{1}{576}[/tex]
[tex]\frac{1}{576}[/tex] probability that the wheel stops a "lose turn" for two successive spins.
c. three successive spins
Three spins, so:
[tex](\frac{1}{24})^3 = \frac{1}{13824}[/tex]
[tex]\frac{1}{13824}[/tex] probability that the wheel stops a "lose turn" for three successive spins.
