Question

A. Overall odds of winning a prize in mega-millions is approximately 1/15, and the numbers in each ticket is independent of the others. Richard bought two mega-million tickets, his probability of winning the first OR the second ticket is:    

1. 0.0667
2. 0.1333
3. 0.1289

B. The data indicate that 10.5% of people with a Cardiovascular Disease who were diagnosed with COVID-19 died. The data also indicate that this percentage for Diabetes is 7.3%, for Chronic Respiratory Disease is 6.3%, Hypertension is 6%, Cancer is 5.6% and No health conditions is 0.9%. Of patients in a certain COVID-19 treatment center, 35% have cardiovascular diseases, 15% have diabetes, 20% have chronic respiratory diseases, 15% have hypertension, 4% have cancer and the other 11% have no health conditions. The total mortality rate at this treatment center should be:

                   

1. 36.6%
2. 9.3%
3. 16.7%

C. An engineering student wants to select a carbon steel workpiece for a prototype of a robot arm. There are multiple material properties that should be considered, therefore the student decided to assume that the all the Carbon Steels listed in the table as homogeneous for Brinell Hardness. Which of the following statement(s) is (are) true about outliers of Brinell Hardness?    

    

1. 1095 normalized at 1650 F is a low outlier

2. 1030 quench & temper at 400 F is a high outlier

3. 1050 quench & temper at 400 F is a high outlier

1. Only (i) is correct
2. Only (i) and (iii) are correct
3. Only (ii) and (iii) are correct

Answer 1

A.

P( winning the first ticket) = P(A)= 1/15

P( winning the second ticket) = P(B) = 1/15

P ( winning both) = P( A and B) = P(A)P(B) {SInce A and B are independent} = 1/15*1/15 =1/225

P( winning first or second) =

P(A or. B) = P(A) + P(B) - P(A and B)

=1/15 + 1/15 - 1/225

=2/15 - 1/225

= 0.1289