The table below shows the results of a survey in which 146 families were asked i
ID: 3170499 • Letter: T
Question
The table below shows the results of a survey in which 146 families were asked if they own a computer and f they will be taking a summer vacation this year. Find the probability that a randomly selected family is not taking a summer vacation this year. The probability is. (Round to the nearest thousandth as needed.) Find the probability that a randomly selected family owns a computer. The probability is. (Round to the nearest thousandth as needed.) Find the probability a randomly selected family is taking a summer vacation this year given that they own a computer. The probability is. (Round to the nearest thousandth as needed.) Find the probability a randomly selected family is taking a summer vacation this year and owns a computer. The probability is. (Round to the nearest thousandth as needed.)Explanation / Answer
Solution:
Vacation
No Vacation
Total
Computer
46
10
56
No Computer
56
34
90
Total
102
44
146
P(No Vacation) = 44/146 = 0.30137
P(Computer) = 56 / 146 = 0.38356
P(Vacation | Computer) = 46 / 56 = 0.82143
P(Vacation and Computer ) = 46 /146 = 0.31507
To events are considered independent if P(A and B ) = P(A)*P(B)
P ( Vacation ) * P (Computer ) = (102/146)*(56/146) = 0.26797
Since 0.27 does not equal 0.31, the events are dependent.
Vacation
No Vacation
Total
Computer
46
10
56
No Computer
56
34
90
Total
102
44
146