Midterm large crosstab solution

a) P(mutual fund | banker) = 14/49 = 28.57%

b) P(stock and lawyer) = 23/150 = 15.33%

c) P(not oil/gas exec or money market)

= P(not oil/gas exec) + P(money market) – P(not oil/gas exec and money market)

= (49+42)/150 + 46/150 – (31+8)/150 = 98/150 = 65.33%

d) P(not stock | banker) = 100% - P(stock | banker) = 100% - 4/49 = 91.84%

e) P(not lawyer and not mutual fund) = (7+33+31+4)/150 = 75/150 = 50%

f) P(not oil/gas exec | not money market) = (14+4+11+23)/(44+60) = 52/104 = 50%

g) P(stock or banker) = P(stock) + P(banker) – P(stock and banker)

= 60/150 + 49/150 – 4/150 = 105/150 = 70%

h) Left side: P(lawyer and mutual fund) = 11/150 = 0.0733

Right side: P(lawyer)*P(mutual fund) = (42/150)(44/150) = 0.0821

The two sides are unequal. Therefore, they are not independent events.