Question

1) According to a survey of households in a particular​ country, the probability that the residents own 2 cars if their annual household income is over​ $50,000 is​ 80%. Of the households​ surveyed, 60% had incomes over​ $50,000 and​ 70% had 2 cars. Find the probability that the residents of a household own 2 cars and have an income over​ $50,000 a year.

A. 0.12

B. 0.48

C. 0.22

D. 0.18

2) The closing price of a​ company's stock tomorrow can be​ lower, higher or the same as​ today's closing price. Based on the closing price of the stock collected over the last​ month, 25% of the days the closing price was higher than previous​ day's closing​ price, 45% was lower than previous​ day's and​ 30% was the same as previous​ day's. Based on this​ information, the probability that​ tomorrow's closing price will be higher than​ today's is​ 25%. What probability approach is this an example​ of?

A. A priori probability

B. Subjective probability

C. Conditional probability

D. Empirical probability

3) The probability that a new advertising campaign will increase sales is assessed as being 0.80. The probability that the cost of developing the new ad campaign can be kept within the original budget allocation is 0.40. Assuming that the two events are​ independent, find the probability that the cost is kept within budget or the campaign will increase sales.

A. 0.88

B. 0.32

C. 0.68

D. 0.20

4) A company has 2 machines that produce widgets. An older machine produces​ 23% defective​ widgets, while the new machine produces only​ 8% defective widgets. In​ addition, the new machine produces 3 times as many widgets as the older machine does. What is the probability that a randomly chosen widget produced by the company is​ defective?

A. 0.1175

B. 0.156

C. 0.078

D. 0.310

Answer 1

Answer:

1.

Given,

P(A) = 0.70

P(A') = 1 - P(A) = 1 - 0.70

= 0.30

P(B) = 0.60

P(B') = 1 - P(B)

= 1 - 0.60

= 0.40

P(A|B) = 0.80

consider,

P(A|B) = P(A and B)/P(B)

substitute values

0.80 = P(A and B)/0.60

P(A and B) = 0.80*0.60

P(A and B) = 0.48

Now,

P(A' and B) = P(B) - P(A and B)

substitute values

= 0.60 - 0.48

= 0.12

So Option A is right answer i.e., 0.12.

4.

To give the required probability

P(A|B) = 8% = 0.08

P(A|B') = 23% = 0.23

P(B) = 0.75

consider,

P(A) = P(A and B) + P(A and B')

where as P(A and B) = P(A|B)*P(B)

substitute values

= 0.08*0.75 + 0.23*(1-0.75)

= 0.08*0.75 + 0.23*0.25

= 0.06 + 0.0575

= 0.1175

Option A is right answer.

Please post the remaining questions as separate post. Thank you.