Question

I really stuck on this question.

A car dealer sold 630 automobiles last year. The following table categorizes the cars sold by size and color and presents the number of cars in each category. A car is to be chosen at random from the 630 for which the owner will win a lifetime of free oil changes. Give your answer as a fraction and as a decimal (up to 4 decimal places) in the given spaces.

	White	Black	Red	Grey	Total
Small	92	61	23	124	300
Midsize	76	53	26	95	250
Large	16	22	12	30	80
Total	184	136	61	249	630

g. Determine whether color and size are independent. Justify your answer by showing your work here. (HINT: Use multiplication rule or conditional probabilities from above)

Answer 1

Answer (g)

we know that two events A and B are independent only when P(A and B) = P(A)*P(B)

let us consider white color as event A and small size as event B

then using the data table,

P(A) = (number of white cars sold)/(total number of cars sold)

= 184/630

= 0.2921

and

P(B) = (number of small size cars sold)/(total number of cars sold)

= 300/630

= 0.4762

And

P(A and B) = (number of small sized white cars sold)/(total number of cars sold)

= 92/630

= 0.1460

checking whether P(A and B) = P(A)*P(B)

setting the calculated probabilities, we get

0.1460 0.2921*0.4762

0.1460 0.1391

so, white and small size are not independent

therefore, we can say that color and size are not independent