Question

A carnival game wheel has 12 equal sections. One of the sections contains a star. To win a prize, players must land on the section with the star on two consecutive spins. What is the probability of a player winning?

Answer 1

`P("winning") = 1/144`

Explanation:

`P("winning")`

`color(white)("XXX")P("star on second spin" | "star on first spin") xx P("star of first spin")`

`P("star on first spin")= 1" out of "12 = 1/12`

`P("star on second spin given star on first spin") =1" out of " 12 =1/12`
(Note that getting a star on the second spin is actually independent of what happened on the first spin)

Therefore
`color(white)("XXX")P("winning")=1/12 xx 1/12=1/144`