Three hundred twelve viewers were asked if they were satisfied with TV coverage of a recent disaster.
Gender
Female Male
Satisfied 90 53
Not Satisfied 124 45
(a) Find P(satisfied). (Give your answer correct to two decimal places.)
(b) Find P(satisfied | female). (Give your answer correct to two decimal places.)
(c) Find P(satisfied | male). (Give your answer correct to two decimal places.)
To find the answers to these probability questions, we can use the information given in the table.
(a) To find P(satisfied), we need to calculate the proportion of viewers who were satisfied out of the total number of viewers.
Total number of viewers = 312
Number of viewers satisfied = 90 (from the table)
P(satisfied) = (Number of viewers satisfied) / (Total number of viewers)
P(satisfied) = 90 / 312
P(satisfied) ≈ 0.29 (rounded to two decimal places)
Therefore, P(satisfied) is approximately 0.29.
(b) To find P(satisfied | female), we need to calculate the proportion of female viewers who were satisfied out of the total number of female viewers.
Total number of female viewers = 214 (from the table)
Number of female viewers satisfied = 90 (from the table)
P(satisfied | female) = (Number of female viewers satisfied) / (Total number of female viewers)
P(satisfied | female) = 90 / 214
P(satisfied | female) ≈ 0.42 (rounded to two decimal places)
Therefore, P(satisfied | female) is approximately 0.42.
(c) To find P(satisfied | male), we need to calculate the proportion of male viewers who were satisfied out of the total number of male viewers.
Total number of male viewers = 98 (from the table)
Number of male viewers satisfied = 53 (from the table)
P(satisfied | male) = (Number of male viewers satisfied) / (Total number of male viewers)
P(satisfied | male) = 53 / 98
P(satisfied | male) ≈ 0.54 (rounded to two decimal places)
Therefore, P(satisfied | male) is approximately 0.54.