JEE Main Math Class 12 Probability Part 1 Questions

If the outcome is one of the following:
H, TTH, TTTTH, ..., then X wins.
As subsequent tosses are independent, so the probability that X wins is
p+

p

4

+

p

16

+....=

4p

3

Similarly Y wins if the outcome is one of the following: TH, TTTH, TTTTTH, ...
Therefore, the probability that Y wins is

1−p

2

+

1−p

8

+

1−p

32

=

2(1−p)

3

Since, the probability of winning the game by both the players is equal then, we have

4p

3

=

2(1−p)

3

⇒p=

1

3