A fair faces die is rolled repeatedly until a number less than appears. If the mean of the number of tosses required is , then is equal to ___.

10 Explanation: 1. Probability of Success ( ): Humein tab tak die roll karni hai jab tak se chhota number na aa jaye. Die par faces hain. se chhote numbers hain. Isliye, success ki probability ( ) hogi: 2. Geometric Distribution aur Mean: Yeh ek geometric distribution ka case hai jahan hum "first success" tak trials count kar rahe hain. Geometric distribution ka mean (expected value) hota hai: 3. Equation Banana: Sawal ke anusar, mean diya gaya hai. Isliye: ki value substitute karne par: 4. ki Value Nikalna: Kyunki hai, hum dono side se ko cancel kar sakte hain: Final Answer The value of is 10 .

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JEE 2023 — Mathematics PYQ

JEE | Mathematics | 2023

A fair $n(n > 1)$ faces die is rolled repeatedly until a number less than $n$ appears. If the mean of the number of tosses required is $\frac{n}{9}$ , then $n$ is equal to ___.

JEE 2023 — Mathematics PYQ

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