Answer to Question #176747 in Statistics and Probability for kris

Question

In a town, the probabilities that a family owns a microwave, an air conditioner and a computer are 0.5, 0.6, and 0.8 respectively.

A)If a family is chosen at random from the town, find the probability that the family chosen owns

(i) all three items

(ii) only a microwave and an air conditioner

(iii) none of the three it

Answer 1

Let's designate events:

A - the family owns a microwave

B - the family owns an air conditioner

C - the family owns a computer

Then $p(A) = 0.5,\,\,p(B) = 0.6,\,\,p(C) = 0.8$

i) Find the probability that the family owns both a microwave oven and an air conditioner and a computer.

$p = p(A)p(B)p(C) = 0.5 \cdot 0.6 \cdot 0.8 = 0,24$

Answer: p=0.24

ii) The wanted probability is:

$p = p(A)p(B)(1 - p(C)) = 0.5 \cdot 0.6 \cdot (1 - 0.8) = 0,06$

Answer: p=0.06

iii) The wanted probability is:

$p = (1 - p(A))(1 - p(B))(1 - p(C)) = (1 - 0.5) \cdot (1 - 0.6) \cdot (1 - 0.8) = 0,04$

Answer: p=0.04