Leila is playing a carnival game in which she is given 4 chances to throw a ball through a hoop. If her chance of success on each throw is 1/5, what is the chance that she will succeed on at least 3 of the throws?
Choose the correct option.
A) 1/5^4  B) 1/5^3  C) 6/5^4  D) 13/5^4  E) 17/5^4
Probability that She will succeed on at least 3 of the throws = Probability that she will succeed on exactly 3 throws + probability that she will succeed on atleast 4 throws.   Probability that she will succeed on exactly 3 throws:   S - succeed   F - Failure   So there are 4 possibilities   FSSS , SFSS, SSFS, SSSF   Probability os success = 1/5   Probability of failure= 1 - probability of success = 1- 1/5 = 4/5   Probability of success on at least three tries =   Probability that she will succeed on exactly 3 throws + probability that she will succeed on atleast 4 throws =   P(FSSS) + P(SFSS) + P(SSFS) + P(SSSF) + P(SSSS) =   {(4/5) *(1/5) *(1/5) *(1/5)} + {(1/5) *(4/5) *(1/5) *(1/5)} + {(1/5) *(1/5) *(4/5) *(1/5)} + {(1/5) *(1/5) *(1/5) *(4/5)} + {(1/5) *(1/5) *(1/5) *(1/5)} =   (1/5)*(1/5)*(1/5)* { (4/5) + (4/5) + (4/5) + (4/5) + (1/5) }   = 17 / 5^4   Answer:17/5^4
<result>E</result>
Leila is playing a carnival game in which she is given 4 chances to throw a ball through a hoop. If her chance of success on each throw is 1/5, what is the chance that she will succeed on at least 3 of the throws?