An unbiased coin is tossed repeatedly until the outcome of two successive…
2005
An unbiased coin is tossed repeatedly until the outcome of two successive tosses is the same. Assuming that the trials are independent, the expected number of tosses is
- A.
3
- B.
4
- C.
5
- D.
6
Attempted by 4 students.
Show answer & explanation
Correct answer: A
The first toss is compulsory. After the first toss, every subsequent toss is compared with the immediately previous toss.
For any current previous outcome, the probability that the next toss is the same is 1/2. Therefore the number of additional tosses needed after the first toss follows a geometric distribution with success probability p = 1/2.
Expected additional tosses = 1/p = 2.
Expected total number of tosses = 1 + 2 = 3.