Question

1. The following table shows the results of a survey in which 104 families were asked if they own a computer and if they will be taking a summer vacation this year.

	Summer vacation - YES	Summer vacation - NO
Own a computer	35	10
Don’t own a computer	42	17

1. The probability a randomly selected family is taking a summer vacation this year is _____

2. The probability a randomly selected family doesn’t own a computer is ______

3. The probability a randomly selected family doesn’t own a computer and is taking a summer vacation this year is ______

4. The probability a randomly selected family doesn’t own a computer or is taking a summer vacation this year, or both is ______

5. If a randomly selected family is not taking a summer vacation this year, the probability the selected family owns a computer is _____

Answer 1

(i) The probability a randomly selected family is taking a summer vacation this year is computed as:
= n(summer vacation - yes ) / Total families
= (35 + 42)/104
= 77/104
= 0.7404

Therefore 0.7404 is the required probability here.

(ii) The probability a randomly selected family doesn’t own a computer is computed here as:
= n(dont own computer) / Total families
= (42 + 17)/104
= 59/104
= 0.5673

Therefore 0.5673 is the required probability here.

(iii) The probability a randomly selected family doesn’t own a computer and is taking a summer vacation is computed here as:
= n(no computer and taking summer vacation ) / Total families
= 42/104
= 0.4038

Therefore 0.4038 is the required probability here.

(iv) The probability a randomly selected family doesn’t own a computer or is taking a summer vacation this year is computed as:
= n(No computer ) + n(computer and summer vacation ) / Total families
= (59 + 35) / 104
= 94/104
= 0.9038

Therefore 0.9038 is the required probability here.

(v) Given that a randomly selected family is not taking a summer vacation this year, probability the selected family owns a computer is computed using bayes theorem as:
P( owns computer | no summer vacation) = n(owns computer and no summer vacation ) / n(no summer vacation ) = 10/27 = 0.3704

Therefore 0.3704 is the required probability here.