Question
Consider an experiment of tossing a coin repeatedly until the outcomes of two consecutive tosses are same. If the probability of a random toss resulting in head is 1 3 , then the probability that the experiment stops with head is
JEE Advanced
Mathematics
Probability
2023
JEE Advanced 2023 (Paper 2)
JEE Advanced Mathematics Question (2023) — Solution
Options
- A. 1 3
- B. 5 21
- C. 4 21
- D. 2 7
Answer
B. 5 21
Step-by-step solution
Given, P ( H ) = 1 3 So, P ( T ) = 1 - 1 3 = 2 3 Now probability of the event is given by, P ( E ) = P ( H H ) + P ( T H H ) + P ( H T H H ) + P ( T H T H H ) + P ( H T H T H H ) + P ( T H T H T H H ) + … ⇒ P ( E ) = 1 3 × 1 3 + 2 3 × 1 3 × 1 3 + 1 3 × 2 3 × 1 3 × 1 3 + 4 3 5 + 4 3 6 + 8 3 7 + 8 3 8 + … ⇒ P ( E ) = 1 3 2 + 2 3 3 + 2 3 4 + 4 3 5 + 4 3 6 + 8 3 7 + 8 3 8 + … ⇒ P ( E ) = 1 3 2 + 2 3 4 + 4 3 6 + … . + 2 3 3 + 4 3 5 + 8 3 7 + … . ⇒ P ( E ) = 1 3 2 1 - 2 3 2 + 2 3 3 1 - 2 3 2 ⇒ P ( E ) = 1 7 + 2 21 = 5 21
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