The table shows the results of a survey of 100 authors by a publishing company. ...

The table shows the results of a survey of 100 authors by a publishing company.

	New Authors	Established Authors	Total
Successful	10	30	40
Unsuccessful	10	50	60
Total	20	80	100

Compute the following conditional probability.

An author is established, given that she is successful.

2) The table shows the results of a survey of 100 authors by a publishing company.

	New Authors	Established Authors	Total
Successful	15	25	40
Unsuccessful	10	50	60
Total	25	75	100

Compute the following conditional probability.

An unsuccessful author is established.

Solutions

Expert Solution

	New Authors	Established Authors	Total
Successful	10	30	40
Unsuccessful	10	50	60
Total	20	80	100

P[ An author is established, given that she is successful ] = P[ An author is established and she is successful ] / P[ she is successful ]

P[ she is successful ] = Number of successful author / Total number of authors

P[ she is successful ] = 40/100

P[ An author is established and she is successful ] = Number of established and successful author / Total number of authors

P[ An author is established and she is successful ] = 30/100

P[ An author is established, given that she is successful ] = ( 30/100)/(40/100)

P[ An author is established, given that she is successful ] =3/4

P[ An author is established, given that she is successful ] = 0.75

	New Authors	Established Authors	Total
Successful	15	25	40
Unsuccessful	10	50	60
Total	25	75	100

P[ An author is established given she is unsuccessful ] = P[ An author is established and she is unsuccessful ] / P[ she is unsuccessful ]

P[ An author is established and she is unsuccessful ] = Number of established and unsuccessful authors / Total number of authors

P[ An author is established and she is unsuccessful ] = 50/100

P[ she is unsuccessful ] = Number of unsuccessful authors / Total number of authors

P[ she is unsuccessful ] = 60/100

P[ An author is established given she is unsuccessful ] = (50/100)/(60/100)

P[ An author is established given she is unsuccessful ] = 5/6

P[ An author is established given she is unsuccessful ] = 0.8333

orchestra answered 1 year ago

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