JEE Advanced · 2009 · 12 Apr 2009 · Paper 1 · Probability XII

A fair die is tossed repeatedly until a six is obtained. Let

X

denote the number of tosses required.

The probability that

X = 3

equals

(A) $\frac{25}{216}$ ✓ Correct
(B) $\frac{25}{36}$
(C) $\frac{5}{36}$
(D) $\frac{125}{216}$

Answer: (A)

Solution

For

X = 3

, we need:

First toss: not a six (probability $\frac{5}{6}$ )
Second toss: not a six (probability $\frac{5}{6}$ )
Third toss: a six (probability $\frac{1}{6}$ )

Therefore:

P (X = 3) = \frac{5}{6} \times \frac{5}{6} \times \frac{1}{6} = \frac{25}{216}

JEE Advanced · 2009 · 12 Apr 2009 · Paper 1 · Single correct option

Practise more: all JEE Advanced PYQs on Probability XII →

More JEE Advanced questions on Probability XII

Suppose that Box I contains 6 red balls and 9 green balls, and Box II contains 8 red balls and 12 green balls. All the balls of Box I and Box II are mixed together and a ball is chosen at random from them. Let $E_{1}$ be the event that the ball chosen belonged to Box I …
JEE Advanced 2026View solution →
A bookshelf contains 6 distinct books of Mathematics and 5 distinct books of Physics. From these 11 books, 6 books are chosen at random. Let X be the absolute value of the difference between the number of Mathematics books chosen and the number of Physics books chosen. If …
JEE Advanced 2026View solution →
Three students $S_{1}, S_{2}$ and $S_{3}$ are given a problem to solve. Consider the following events :
$U :$ At least one of $S_{1}, S_{2}$ and $S_{3}$ can solve the problem,
$V : S_{1}$ can solve the problem, given that neither $S_{2}$ nor …
JEE Advanced 2025View solution →
A factory has a total of three manufacturing units, $M_{1}, M_{2}$ , and $M_{3}$ , which produce bulbs independent of each other. The units $M_{1}, M_{2}$ , and $M_{3}$ produce bulbs in the proportions of 2: 2: 1, respectively. It is known that 20% of the bulbs produced in …
JEE Advanced 2025View solution →
A bag contains $N$ balls out of which 3 balls are white, 6 balls are green, and the remaining balls are blue. Assume that the balls are identical otherwise. Three balls are drawn randomly one after the other without replacement. For $i = 1, 2, 3$ , let $W_{i}, G_{i}$ , and $B_{i}$ deno …
JEE Advanced 2024View solution →
A student appears for a quiz consisting of only true-false type questions and answers all the questions. The student knows the answers of some questions and guesses the answers for the remaining questions. Whenever the student knows the answer of a question, he gives the correct …
JEE Advanced 2024View solution →