Question

1. The following table gives the families with a combined income compared to each level of educational attainment (Source: US Department of Commerce, Census Bureau, Current Population)

X	Under $20K	$20K- $49,999	$50K - $99999	$100K - $149999	$150K- $199999	$200K +
High School or Less	4,200	9,581	9,115	3,271	1,080	750
Some College	1,816	5,723	7,826	4,181	1,756	1,205
Bachelors	1,691	5,729	13,278	10,972	7,029	9,382
Masters	223	673	1,995	2,028	1,466	2,039
PhD	36	112	352	363	327	714

1. What is the probability that a randomly selected family has an income of $150,000 or more?
2. What is the probability that a randomly selected family achieved a Bachelors degree?
3. What is the probability that a randomly selected family has Some College education and have an income of $50K-$99,999?
4. What is the probability that a randomly selected family achieved a Masters degree or a PhD?
5. What is the probability that a randomly selected family makes $100K- $149,999 given the family achieved a Bachelors degree?
6. What is the probability that a randomly selected family making $200K or more has a high school or less education?
7. Are the events "Bachelors" degree and "Under 20K" income Independent? Answer Yes or No and back up your answer with one of the independence equations.

Answer 1

X	Under $20K	$20K- $49,999	$50K - $99999	$100K - $149999	$150K- $199999	$200K +	Total
High School or Less	4,200	9,581	9,115	3,271	1,080	750	27,997
Some College	1,816	5,723	7,826	4,181	1,756	1,205	22,507
Bachelors	1,691	5,729	13,278	10,972	7,029	9,382	48,081
Masters	223	673	1,995	2,028	1,466	2,039	8,424
PhD	36	112	352	363	327	714	1,904
total	7,966	21,818	32,566	20,815	11,658	14,090	1,08,913

a)

probability that a randomly selected family has an income of $150,000 or more =(11658+14090)/108913

=25748/108913

b)

probability that a randomly selected family achieved a Bachelors degree =48081/108913

c)

e probability that a randomly selected family has Some College education and have an income of $50K-$99,999 =7826/108913

d)

probability that a randomly selected family achieved a Masters degree or a PhD

=(8424+1904)/108913=10328/108913

e)

probability that a randomly selected family makes $100K- $149,999 given the family achieved a Bachelors degree =10972/48081

f)

probability that a randomly selected family making $200K or more has a high school or less education =750/14090

g)

here P(Bachelor)=48081/108913=0.441462

while P(Bachelor|under $20K)=1691/7966=0.212277

as both are different ; therefore this events are not independent,