The table below shows the results of a survey in which 146 families were asked i

Question

The table below shows the results of a survey in which 146 families were asked if they own a computer and if they will be taking a vacation this year.

Summer vacation this year
yes no total
Own yes 46 10 56
a no 56 34 90
Comp. total 102 44 146

a.) find probability that a randomly selected family is not taking a summer vacation this yr. (round to nearest thousandth)
b.) find the probability that a randomly selected family owns a computer
c.) find the probability that a randomly selected family is taking a summer vacation this yr given that they own a computer.
d.) find the probability that a randomly selected family is taking a vacation this year and owns a computer.
e.) are the events of owning a computer and taking a summer vacation this year independent or dependent events?

Explanation / Answer

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.

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