According to a recent report, 30% of new businesses in 2013 were started by wome

Question

According to a recent report, 30% of new businesses in 2013 were started by women and 70% of new businesses in 2013 were started by men. In 2013, 10% of new businesses started by women had revenues of $50,000 and above, whereas 12% of new businesses started by men had revenues of $50,000 and above. Complete parts (a) and (b) below.

a. If a new business started in 2013 is selected at random and the new business had revenues of $50,000 and above, what is the probability that the new business was started by a woman?

nothing

(Round to three decimal places as needed.)

b. If a new business started in 2013 is selected at random, what is the probability that the new business had revenues of $50,000 and above?

nothing

(Round to three decimal places as needed.)

Explanation / Answer

Ans:

Given that

P(new business Women)=0.3

P(new business men)=0.7

P(above 50000/new business women)=0.1

P(above 50000/new business men)=0.12

a)First find out

P(above 50000)=0.1*0.3+0.12*0.7=0.114

Using Bayes theorm:

P(new business women/above 50000)=(0.1*0.3)/0.114=0.263

b)

P(above 50000)=0.1*0.3+0.12*0.7=0.03+0.084=0.114

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