During a particular equestrian competition, the rider and his horse have 5 fences to jump. If the rider falls off during a jump, the rider is disqualified. The probability of the rider falling off on a jump is 12/35. What is the least number of fences that the rider can jump before the probability of falling off at least once is more than 50%. Select:
A) 1
B) 5
C) 4
D) 2
E) 3
Rule of Subtraction: P(A) = 1 - P(A')   Rule of Multiplication: P(A ∩ B) = P(A) P(B)   The probability that the rider falls at least once in 2 jumps is 1- (23/35)^2 = 1 - 529/1,225 = 696/1,225 &lt; 50%.   The probability that the rider falls at least once in 3 jumps is 1- (23/35)^3 = 1 - 12,167/42,875 = 30,708/42,875 &gt; 50%.   Answer: 3
<result>E</result>
During a particular equestrian competition, the rider and his horse have 5 fences to jump. If the rider falls off during a jump, the rider is disqualified. The probability of the rider falling off on a jump is 12/35. What is the least number of fences that the rider can jump before the probability of falling off at least once is more than 50%.