Question

1. Imelda has a large collection of shoes. She has 20 pairs of sneakers of which: 9 pairs are canvas and 11 are leather; 8 pairs are white, 7 are black, and 5 are red; 5 pairs are white and canvas, 1 pair is black and canvas, and 2 pairs are red and leather. Suppose Imelda selects a pair of sneakers at random from this collection of 20 pairs.

a) What is the probability that she selects a red canvas pair?

b) Given that the pair she selected is canvas, what is the probability that they are red?

c) Given that the pair she selected is red, what is the probability that they are canvas?

d) What is the probability that she selects a white leather pair?

e) Given that the pair she selected is white, what is the probability that they are leather?

f) Given that the pair she selected is leather, what is the probability that they are white?

Answer 1

Based on data provided following table was prepared:

	Leather	Canvas	Total
White	3	5	8
Red	2	3	5
Black	6	1	7
Total	11	9	20

Answer a)

Based on table, it can be seen that

No. of red canvas pair = 3

Total no. of sneakers = 20

Probability that she selects a red canvas pair = 3/20 = 0.15

Answer b)

We have to find P(Red | Canvas)

P(Red | Canvas) = P(Red AND Canvas)/P(Canvas)

Based on table, it can be seen that

No. of canvas sneakers = 9

P(Canvas) = 9/20 = 0.45

No. of red canvas pair = 3

P(Red AND Canvas) = 3/20 = 0.15

P(Red | Canvas) = 0.15/0.45 = 0.3333

Given that the pair she selected is canvas, the probability that they are red is 0.3333

Answer c)

We have to find P(Canvas | Red)

P(Canvas | Red) = P(Red AND Canvas)/P(Red)

Based on table, it can be seen that

No. of red sneakers = 5

P(Red) = 5/20 = 0.25

P(Red AND Canvas) = 0.15 (Refer to Part b)

P(Canvas | Red) = 0.15/0.25 = 0.60

Given that the pair she selected is red, the probability that they are canvas is 0.60

Answer d)

Based on table, it can be seen that

No. of white leather pair = 3

Total no. of sneakers = 20

Probability that she selects a white leather pair = 3/20 = 0.15

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