Verified Solution • 2025–26 Session moderate

QJEEM23Ma7404: JEE Main 2023 Mathematics - Class 12 JEEM23Ma7404 Solution: A bag contains six balls of different colours. Two balls are…

A bag contains six balls of different colours. Two balls are drawn in succession with replacement. The probability that both the balls are of the same colour is p. Next four balls are drawn in succession with replacement and the probability that exactly three balls are of the same colour is qq . If p:q=m:np: q=m: n , where mm and nn are coprime, then m+nm+n is equal to :

Step-by-Step Verified Solution

p=636=16p = {6 \over {36}} = {1 \over 6}

q=6C1×5C1×4!3!64=1201296=554q = {{{}^6{C_1} \times {}^5{C_1} \times {{4!} \over {3!}}} \over {{6^4}}} = {{120} \over {1296}} = {5 \over {54}}

pq=16554=546×5=95=mn{p \over q} = {{{1 \over 6}} \over {{5 \over {54}}}} = {{54} \over {6 \times 5}} = {9 \over 5} = {m \over n}

m+n=14m + n = 14

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