Teaching Haryana (HPSC) Assistant Professor Mock Test 2025 Mathematical Science Statistics & Exploratory Data Analysis
Imagine a game where you roll a fair six-sided die repeatedly until a 6 appears. Let X be the number of rolls needed. You are also supposed to flip a fair coin until you get a head. Let Y be the count of the number of coin flips required. Which of the following is the correct expression for computing P(X > Y)?
1
\(∑_{j=1}^∞ [(\frac{5}{6})^{j-1}(\frac{1}{2})^j * ∑_{i=0}^{j-1} (\frac{1}{2})^i]\)
2
\(∑_{j=1}^∞ [(\frac{5}{6})^{j-1} * ∑_{i=0}^{j-1} (\frac{1}{2})^i]\)
3
\(∑_{j=1}^∞ [(\frac{1}{6})*(\frac{5}{6})^{j-1} * ∑_{i=1}^{j-1} (\frac{1}{2})^i]\)
4
\(∑_{j=1}^∞ [(\frac{1}{6})^{j-1} * ∑_{i=0}^{j-1} (\frac{1}{2})^i]\)
5
Question Not Attempted