If a coin is tossed a sequence of times, what is the probability that the first head will occur after the fifth toss, given that it has not occurred in the first two tosses?
The probability of getting a head after tossing a coin is ½. The complement of that is ½ as well. We will stimulate 6 tosses, with the sixth toss displaying the head.
P(X=1)=1/2 = 1/2
P(X=2)=(1/2)(1/2)= 1/4
P(X=3)=(1/2)(1/2)(1/2) 1/8
P(X=4)= (1/2) (1/2) (1/2) (1/2) 1/16
P(X=5)= (1/2) (1/2) (1/2) (1/2) (1/2) = 1/32
P(X=6)= (1/2) (1/2) (1/2) (1/2) (1/2)(1/2) = 1/64
The probability that the first head will occur after the fifth toss, given that it has not occurred in the first two tosses is 1/64.