Please show all work so I can learn The following table clas

Please show all work so I can learn!

The following table classifies 1000 college graduates by area of concentration in college and type of employer for whom they went to work after graduation.

Types of Employer

Major

Public Accounting
A₁

Banking & Finance
A₂

Electronics
A₃

Merchandising
A₄

All Others
A₅

Total

Accounting B₁

60

15

10

5

10

100

General Business B₂

20

50

10

65

5

150

Humanities B₃

1

2

2

10

60

75

Social Studies B₄

2

20

8

20

70

120

Engineering B₅

2

5

188

5

50

250

All Others B₆

30

50

55

60

110

305

Total

115

142

273

165

305

1,000

Evaluate following probabilities:

P (B3)

P (B3 and A4)

P (A4) * P (B3/A4)

P (A1 I B1)

	Types of Employer
Major	Public Accounting A1	Banking & Finance A2	Electronics A3	Merchandising A4	All Others A5	Total
Accounting B1	60	15	10	5	10	100
General Business B2	20	50	10	65	5	150
Humanities B3	1	2	2	10	60	75
Social Studies B4	2	20	8	20	70	120
Engineering B5	2	5	188	5	50	250
All Others B6	30	50	55	60	110	305
Total	115	142	273	165	305	1,000

Solution

P(B3) = 75/1000 = 0.075

P(B3 and A4) = 10/1000 = 0.01

{P (A4) * P (B3 | A4) = P(A4 and B3) = 0.01

P(A1 | B1) = #A1 and B1 / #B1 = 60/100 = 0.6