Advanced Probability Calculator

Example: Probability of drawing a heart OR a king from a deck

P(Heart) = 13/52, P(King) = 4/52, P(Heart AND King) = 1/52

P(Heart OR King) = 13/52 + 4/52 - 1/52 = 16/52

Example: Probability of having rain given cloudy skies

P(Rain) = 0.3, P(Cloudy) = 0.4, P(Rain AND Cloudy) = 0.2

P(Rain|Cloudy) = P(Rain AND Cloudy) / P(Cloudy) = 0.2 / 0.4 = 0.5

Example: Probability of getting exactly 3 heads in 5 coin flips

n = 5, p = 0.5, k = 3

P(X=3) = C(5,3) × (0.5)³ × (0.5)² = 10 × 0.125 × 0.25 = 0.3125

Example: Probability of 2 customers arriving in an hour when average is 3 per hour

λ = 3, k = 2

P(X=2) = (e⁻³ × 3²) / 2! ≈ 0.2240

Example: Probability of a value less than 1 in a standard normal distribution

μ = 0, σ = 1, x = 1

P(X < 1) ≈ 0.8413