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.)
a) (90+53)/312 = ?
b) 90/312
c) I'll leave this one for you.
To find the probabilities, we need to calculate the ratios of the number of individuals in each category.
(a) To find P(satisfied):
P(satisfied) = (number of satisfied viewers) / (total number of viewers)
Number of satisfied viewers = 90 (female) + 53 (male) = 143
Total number of viewers = 312
P(satisfied) = 143 / 312 ≈ 0.46 (rounded to two decimal places)
Therefore, P(satisfied) is approximately 0.46.
(b) To find P(satisfied | female):
P(satisfied | female) = (number of satisfied female viewers) / (total number of female viewers)
Number of satisfied female viewers = 90
Total number of female viewers = 90 (satisfied) + 124 (not satisfied) = 214
P(satisfied | female) = 90 / 214 ≈ 0.42 (rounded to two decimal places)
Therefore, P(satisfied | female) is approximately 0.42.
(c) To find P(satisfied | male):
P(satisfied | male) = (number of satisfied male viewers) / (total number of male viewers)
Number of satisfied male viewers = 53
Total number of male viewers = 53 (satisfied) + 45 (not satisfied) = 98
P(satisfied | male) = 53 / 98 ≈ 0.54 (rounded to two decimal places)
Therefore, P(satisfied | male) is approximately 0.54.
To answer these questions, we need to understand some basic concepts in probability. In probability, P(A) denotes the probability of event A occurring, and P(A | B) denotes the conditional probability of event A occurring given that event B has already occurred.
(a) To find P(satisfied), we need to find the probability of being satisfied out of the total viewers. In this case, the total number of viewers is 312, and the number of satisfied viewers is 90 + 53 = 143. Therefore, P(satisfied) = 143/312. Evaluating this expression gives P(satisfied) ≈ 0.46 (rounded to two decimal places).
(b) To find P(satisfied | female), we need to find the probability of being satisfied among the female viewers. In this case, the number of female viewers is 90, and the number of satisfied female viewers is 90. Therefore, P(satisfied | female) = 90/90 = 1.
(c) To find P(satisfied | male), we need to find the probability of being satisfied among the male viewers. In this case, the number of male viewers is 53, and the number of satisfied male viewers is 53. Therefore, P(satisfied | male) = 53/53 = 1.
Hence, the answers are:
(a) P(satisfied) ≈ 0.46
(b) P(satisfied | female) = 1
(c) P(satisfied | male) = 1