If a coin is tossed an infinite number of times with a probability of getting heads each time is 0.55, what is the probability that 5 heads are observed at the 10th toss but not earlier? thanks.
If the fifth head occurs on the tenth toss, the previous nine tosses must include 4 heads and 5 tails.
With the probability of getting a head = 0.55, the probability of getting a tail = 0.45.
Thus the probability that the first nine tosses are 4 heads and 5 tails:
9C4·(0.55)4·(0.45)5 = 0.212757,,,
Following this with a head requires multiplying that answer by 0.55 = 0.117016,,,