Seniors at a certain high school took a survey regarding future plans. All plan

Question

Seniors at a certain high school took a survey regarding future plans. All plan to attend college some time; however, 78% plan to go to college immediately following high school. Of those who plan to attend college immediately following high school, 17% plan to major in Math. Of those who do not plan to attend college immediately following high school, 11% plan to major in Math. What is the probability that a randomly chosen senior does not plan to attend college immediately following high school and plans to major in Math.

a) 0.1100

b) 0.0242

c) 0.8900

d) 0.1700

e) 0.1326

f) None of the above.

A new test to detect TB has been designed. It is estimated that 88% of people taking this test have the disease. The test detects the disease in 97% of those who have the disease. The test does not detect the disease in 99% of those who do not have the disease. If a person taking the test is chosen at random, what is the probability of the test indicating that the person does not have the disease?

a) 0.1452

b) 0.9900

c) 0.0100

d) 0.0300

e) 0.0264

f) None of the above.

Urn A contains 4 yellow balls and 6 red balls. Urn B contains 10 yellow balls and 5 red balls. Urn C contains 11 yellow balls and 12 red balls. An urn is picked randomly (assume that each urn is equally likely to be chosen), and then a ball is picked from the selected urn. What is the probability that the chosen ball came from urn B, given that it was a yellow ball?

a) 0.0813

b) 0.4315

c) 0.0618

d) 0.2589

e) 0.3096

f) None of the above.

Explanation / Answer

Please post 1 question at a time, here' answer to the 1st question in detail. In case you have any doubts please let me know and I'll will be able to help you out with the same.

Let there be 100 students in high school

Hence, 78 plan to go to college immediately following high school., out of which 17% or .17*78 = 13.26 plan to major in Math

22 don't plan to attend collge immidiately following high school, 11% of 22 or 2.42 plan to major in Math.

P(a randomly chosen senior does not plan to attend college immediately following high school and plans to major in Math)

= No. of senior does not plan to attend college immediately following high school and plans to major in Math/ total people

= 2.42/100

= .0242

b) is the correct answer

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