Question

In a certain small town, 65% of the households subscribe to the daily paper, 37% subscribe to the weekly local paper, and 25% subscribe to both papers. Make a two way table to help answer the following: If you know Charlie's neighbor subscribes to as least one paper , What is the probability that the neighbor receives the daily paper?

Answer #1

P[ households subscribe to the daily paper ] = 65% = 0.65

P[ subscribe to the weekly local paper ] = 37% = 0.37

P[ subscribe to both papers ] = 25% = 0.25

Daily paper | Local paper | Total | |

Daily paper | 40% | 25% | 65% |

Local paper | 25% | 12% | 37% |

Total | 65% | 37% |

If you know Charlie's neighbor subscribes to as least one paper , What is the probability that the neighbor receives the daily paper?

P[ At least one paper ] = P[ households subscribe to the daily paper ] + P[ subscribe to the weekly local paper ] - P[ subscribe to both papers ]

P[ At least one paper ] = 0.65 + 0.37 - 0.25

**P[ At least one paper ] = 0.77**

**P[ At least one paper ] = 77%**

P[ Daily paper | At least one paper ] = P[ Daily paper ]/P[ At least one paper ]

**P[ Daily paper | At least one paper ] =
65/77**

**P[ Daily paper | At least one paper ] =
0.8441**

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