Question

The table shows the results of a survey in which 142 men and 145 woman workers age 25 to 64 were asked if they have at least one months income set aside for emergencies. Complete parts a-d. a.) Find the probability that a randomly selected worker has one months income or more set aside for emergencies. b.) Given that a randomly selected worker is male find the probability that the worker has less than one months income. c.) Given that a randomly selected woker has one months income or more, find the probablitly that the worker is female. d.) Are the events "having less than one months income saved" and "being male" independant?

	men	woman	total
less than one months income	65	83	148
one months income or more	77	62	139
total	142	145	287

Answer 1

a.) Find the probability that a randomly selected worker has one months income or more set aside for emergencies.

The number of workers has one months income or more set aside for emergencies = 139

Total workers has set aside for emergencies = 287

Therefore required probability = 139/287 = 0.484321

b.) Given that a randomly selected worker is male find the probability that the worker has less than one months income.

The total number of males = 142

There are 65 workers who are male and less than one month income.

So required probability is = 65/142 = 0.457746

c.) Given that a randomly selected woker has one months income or more, find the probablitly that the worker is female.

The total number of workers who has one months income or more are 139

There are total 62 females who has one months income or more

So the required probability is 62/139 = 0.446043

d) Let's denote the events as

A = workers having less than one months income saved

and B = workers "being male"

THerefore P( A and B) = 65/287 = 0.226481

P(A) = 148/287

P(B) = 142/287

P(A)*P(B) = (148/287)*142/287) = 0.255145 which is not equal to P(A and B)

So the given two events are not independent.

Probability of an event  "having less than one months income saved" is = 148/287