Question

The information in the shows company sizes and sector.

                                                                                                               Company Size

		A (Small)	B (Medium)	C (Large)	Total
	X (Mining)	6	10	9	25
Sector	Y (Warehouse)	23	7	18	48
	Z (Agriculture)	15	8	4	27
	Total	44	25	31	100

b. From the contingency table, state any two non-mutually and two mutually exclusive events.

c. Calculate the following probabilities:
i. That the company selected randomly is in the mining sector.
ii. That the company selected is in warehousing and medium in size.
iii. That the company is in the agriculture or mining sector.
iv. That the company in in the mining sector or large in size.
d. Given that a company falls in the mining sector, calculate the probability that the company is
large.

Answer 1

(b)

(i)

non-mutually exclusive events :

Event 1: Sector X (Mining) and Event 2: Company size A (Small)

(ii)

mutually exclusive events :

Event 1: Sector X (Mining) and Event 2: Sector Y (Warehouse)

(c)

(i)

P(Mining) = 25/100 = 0.25

So,

Answer is:

0.25

(ii)

P(Warehousing AND Medium) = 7/100 = 0.07

So,

Answer is:

0.07

(iii)

P(Agriculture OR Mining) = P(Agriculture) + P( Mining)= 27/100 + 25/100 = 52/100 = 0.52

So,

Answer is:

0.52

(iv)

P( Mining OR Large) = P( Mining) + P(Large) - P(Mining OR Large) = 25/100 + 31/100 - 9/100 = 47/100 = 0.47

So,

Answer is:

0.47

(d)

P(Large/ Mining) = P(Large AND Mining) /P(Mining)

                          = 9/25

                          = 0.36

So,

Answer is:

0.36