ProbabilitymediumPYQ · JEE Main · 6 Apr 2026 · Shift 1 (Morning)Free

Biased-Coin Bag Probability: N = 7 | JEE Main 2026

JEE Maths question with a full step-by-step solution.

Question
A bag contains (N+1)(N+1) coins — NN fair coins, and one coin with 'Head' on both sides. A coin is selected at random and tossed. If the probability of getting 'Head' is 916\dfrac{9}{16}, then NN is equal to
A55
B77correct
C88
D99
Solution
Step 1: NN fair coins (drawn with prob. NN+1\dfrac{N}{N+1}) and 11 two-headed (prob. 1N+1\dfrac{1}{N+1}):
P(Head)=NN+1⋅12+1N+1⋅1.P(\text{Head})=\dfrac{N}{N+1}\cdot\dfrac12+\dfrac{1}{N+1}\cdot1.
 Step 2:
P(Head)=N2(N+1)+22(N+1)=N+22(N+1).P(\text{Head})=\dfrac{N}{2(N+1)}+\dfrac{2}{2(N+1)}=\dfrac{N+2}{2(N+1)}.
 Step 3:
N+22(N+1)=916⇒16(N+2)=18(N+1).\dfrac{N+2}{2(N+1)}=\dfrac{9}{16}\Rightarrow16(N+2)=18(N+1).
⇒16N+32=18N+18⇒14=2N⇒N=7.\Rightarrow16N+32=18N+18\Rightarrow14=2N\Rightarrow N=7.
 Correct answer: (2)
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