# Estimate Probability

## Single Probability Calculator

Formulas:

• Probability of event A occurring P(A) = n(A) / n(S).
• Probability of event A not occurring P(A') = 1 - P(A).
 Number of possible outcomes Number of events occured Probability of event that occurs P(A) Probability of event that does not occurs P(A')

## Multiple Event Probability Calculator

Formulas:

• Probability of event A occurring P(A) = n(A) / n(S).
• Probability of event A not occurring P(A') = 1 - P(A).
• Probability of event B occurring P(B) = n(B) / n(S).
• Probability of event B not occurring P(B') = 1 - P(B).
• Probability of both events occurring P(A ∩ B) = P(A) x P(B).
• Probability of either events occurring P(A ∪ B) = P(A) + P(B) - P(A ∩ B).
• Conditional Probability P(A | B) = P(A ∩ B) / P(B).
 Number of possible outcomes Number of event occurs in A Number of event occurs in B Note: A & B are mutually exclusive events P(A) P(A') P(B) P(B' ) P(A ∩ B) P(A ∪ B) P(A | B)

### Example Multiple Probability Calculation

Find multiple event probabilitiy, given n(s) = 50, n(A) = 10 and n(B) = 5

P(A) = 10/50 = 0.2

P(A') = 1-0.2 = 0.8

P(B) = 5/50 = 0.1

P(B') = 1-0.1 = 0.9

P(A ∩ B) = 0.2 *0.1 = 0.02

P(A ∪ B) = ( 0.2 + 0.1 ) - 0.02 = 0.28

P(A | B) = 0.02 / 0.1 = 0.2