In: Statistics and Probability
(a)
Let X be the number of jumps out of 60 to get an injury.
X ~ Binomial(n = 60, p = 1/60)
Probability that 60 jumps will be completed without an injury = P(X = 0)
= 0.3647923
(b)
Probability that at least one injury will occur in 60 jumps = P(X 1)
= 1 - P(X = 0)
= 1 - 0.3647923
= 0.6352077
(c)
X ~ Binomial(n, p = 1/60)
P(X = 0) 0.70
Taking natural log, we get
n ln(59/60) ln(0.70)
n * -0.01680712 -0.3566749
n 0.3566749 / 0.01680712
n 21.22
Thus, the maximum number of jumps is 21, such that the probability is at least 0.70 when all n jumps will be completed without injury.