# Probability of Events n(A) = 13, n(B) = 4 from n = 52 Find the probability of n(A), n(A'), n(B), n(B'), n(AUB) & n(A∩B) for n(A) = 13, n(B) = 4 from the sample space of total events n = 52. The below is the calculation summary for probability of each function such as P(A), P(A'), P(B), P(B'), P(AUB) & P(A∩B) for events n(A) = 13 & n(B) = 4 from total events of experiment n = 52.

Calculation Summary
Total Events n52
Total Events n(A)13
Total Events n(B)4
P(A)0.25
P(A')0.75
P(B)0.08
P(B')0.92
P(A∩B)0.02
P(AUB)0.31
P(A|B)0.25

## Work with Steps for P(A) & P(B) from n(A) = 13, n(B) = 4 & n = 52

The below is the work with steps shows how to find the probability of P(A), P(A'), P(B), P(B'), P(AUB) & P(A∩B) for n(A) = 13, n(B) = 4 from the total events n = 52 may help grade school students to solve the probability worksheet problems efficiently.
Probability formulas used in this calculation
P(A) = Number of Successful Events / Total Events of Sample Space

P(A) = n(A)/n

P(B) = n(B)/n

P(A∩B) = P(A) x P(B)

P(AUB) = P(A) + P(B) - P(A∩B)
P(A|B) = P(A∩B)/P(B)

P(A') = 1 - P(A)

P(B') = 1 - P(B)

Steps to find P(A) and P(A')
P(A) = 13/52
= 0.25
P(A) = 0.25
P(A') = 1 - P(A)
P(A') = 1 - 0.25
P(A') = 0.75
0.25 is the probability of events n(B) and 0.75 is the probability of not occuring events n(B).

Steps to find P(B) and P(B')
P(B) = 4/52
= 0.08
P(B) = 0.08
P(B') = 1 - P(B)
P(B') = 1 - 0.08
P(B') = 0.92
0.08 is the probability of events n(B) and 0.92 is the probability of not occuring events n(B).

Steps to find P(A∩B)
P(A∩B) = 0.25 x 0.08
= 0.02
P(A∩B) = 0.02
0.31 is the probability of both events n(A) and n(B) occur.

Steps to find P(AUB)
P(AUB) = 0.25 + 0.08 - 0.02
= 0.31
P(AUB) = 0.31
0.31 is the probability of events n(A) or n(B) or both n(A) and n(B) occur.

Steps to find conditional probability P(A|B)
P(A|B) = P(A∩B)/P(B)=0.02/0.08
= 0.25
P(A|B) = 0.25

0.75 is the conditional probability of event n(A) = 13, n(B) = 4 and total events n = 52. 