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