JEE Main 2018 — Probability Question with Solution
From: JEE Main 2018 (Online) 15th April Evening Slot
Question
A player X has a biased coin whose probability of showing heads is p and a player Y has a fair coin. They start playing a game with their own coins and play alternately. The player who throws a head first is a winner. If X starts the game, and the probability of winning the game by both the players is equal, then the value of 'p' is :
Choose an option
Show full solutionCorrect option: B
Correct answer
B
Step-by-step explanation
P(X getting head) = p
P(X getting tail) = 1 - p
P(Y getting head) = P(Y getting tail) =
P(X wins) = p + (1 - p)p + (1 - p)(1 - p)p + ...
=
=
P(Y win) = (1 - p) + (1 - p)(1 - p) + ...
=
According to question,
P(X wins) = P(Y wins)
=
3p = 1
p =
P(X getting tail) = 1 - p
P(Y getting head) = P(Y getting tail) =
P(X wins) = p + (1 - p)p + (1 - p)(1 - p)p + ...
=
=
P(Y win) = (1 - p) + (1 - p)(1 - p) + ...
=
According to question,
P(X wins) = P(Y wins)
=
3p = 1
p =
Practice this on the real CBT interface
Solve this JEE Main question (and the rest of the Probability chapter) on PrepSharp's TCS iON-style CBT player — with timer, bookmarks and session analytics.
Solve interactively →About this question
This is a previous-year question from JEE Main 2018, covering the Probability chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.