Answer:
[tex]\dfrac{25}{216}[/tex]
Step-by-step explanation:
From the given information:
The probability (p) of winning a bottle cap = [tex]\dfrac{1}{6}[/tex]
The probability of not winning a bottle cap will be (q) = 1 - p
[tex]= 1- \dfrac{1}{6}[/tex]
[tex]= \dfrac{5}{6}[/tex]
Since we are told that the winning is placed once on every sixth bottle
Then the required probability = P( of not winning the first purchase) × P( of not winning the second purchase) × P( of winning the third purchase)
[tex]= \dfrac{5}{6} \times \dfrac{5}{6} \times \dfrac{1}{6}[/tex]
[tex]= \dfrac{25}{216}[/tex]
