JEE Main 2026 · 2 Apr · Shift 2 · Mathematics Q8

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MathematicsSingle correct+4 / -1Question 8 of 75

A man throws a fair coin repeatedly. He gets 10 points for each head he throws and 5 points for each tail he throws. If the probability that he gets exactly 30 points is $\dfrac mn$ , $\gcd(m,n)=1$ , then $m+n$ is equal to :

107

105

Answer and worked solution

Official answer: C

Units of 5 points. A head adds 2 and a tail adds 1, each with probability ½. Let $p_k$ be the probability that the running total ever equals exactly $k$ .

Recursion. $p_k=\frac12p_{k-1}+\frac12p_{k-2}$ with $p_0=1$ , $p_1=\frac12$ :
$p_2=\tfrac34,\ p_3=\tfrac58,\ p_4=\tfrac{11}{16},\ p_5=\tfrac{21}{32},\ p_6=\tfrac{43}{64}.$

Answer. 30 points is $k=6$ : $\frac{43}{64}$ , so $m+n=107$ .

(C)

Topics:Classical probability Special series sums

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JEE Main 2026 · 2 Apr · Shift 2, Mathematics question 8