# 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 n | 52 |

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.