Geometric Distribution vs Binomial Distribution

𝐏(𝑋=𝑥; 𝑝) = (1−𝑝)^𝑥−1𝑝

𝐏(𝐗=𝑥; 𝑛,𝑝) = [𝑛!/𝑥!(𝑛-𝑥)!] * 𝑝^𝑥 * (1-𝑝)^(𝑛-𝑥)

• 𝐏(𝑋=𝑛; 𝑝) = (1−𝑝)^𝑛−1𝑝

• 𝐏(𝐗=1; 𝑛,𝑝) = [𝑛!/1!(𝑛-1)!] * 𝑝¹ * (1-𝑝)^(𝑛-1)
• 𝐏(𝐗=1; 𝑛,𝑝) = 𝑛 (1-𝑝)^𝑛-1𝑝
• 𝐏(𝐗=1; 𝑛,𝑝) = 𝑛 𝐏(𝑋=𝑛; 𝑝)

order matters → lower probability

order does not matter → higher probability