2) a) A and B are independent events. 𝑃(𝐴) = 0.25 and 𝑃(𝐵) = 0.4 , Find I. 𝑃(𝐴 ∩ 𝐵′) II. 𝑃(𝐴′ ∩ 𝐵′) III. 𝑃(𝐴 ∪ 𝐵)′ IV. 𝑃
Posted: Sun Jul 10, 2022 11:11 am
2)
a) A and B are independent events. 𝑃(𝐴) = 0.25 and 𝑃(𝐵) = 0.4 ,Find
I. 𝑃(𝐴 ∩ 𝐵′)
II. 𝑃(𝐴′ ∩ 𝐵′)
III. 𝑃(𝐴 ∪ 𝐵)′
IV. 𝑃(𝐴′ ∩ 𝐵)
b) Consider the following table,
If A – The employee is less than 30 years of age.
B – The salary of the employee is less than 30000
What is the probability of 𝑃(𝐵|𝐴) and 𝑃(𝐴|𝐵′) ?
c) A doctor recommended that a patientwith a specific symptom be tested for a particular disease. Theonly evidence the doctor has before the test results are availableis that 10% of people with this symptom have the disease.Experience has shown that this test reveals that 99% of people withthe disease have the disease. The test also reveals that 95% ofpeople who do not have the disease haven’t the disease. If the testreveals the presence of the disease what is the actual probabilitythat the patient has the disease?
a) A and B are independent events. 𝑃(𝐴) = 0.25 and 𝑃(𝐵) = 0.4 ,Find
I. 𝑃(𝐴 ∩ 𝐵′)
II. 𝑃(𝐴′ ∩ 𝐵′)
III. 𝑃(𝐴 ∪ 𝐵)′
IV. 𝑃(𝐴′ ∩ 𝐵)
b) Consider the following table,
If A – The employee is less than 30 years of age.
B – The salary of the employee is less than 30000
What is the probability of 𝑃(𝐵|𝐴) and 𝑃(𝐴|𝐵′) ?
c) A doctor recommended that a patientwith a specific symptom be tested for a particular disease. Theonly evidence the doctor has before the test results are availableis that 10% of people with this symptom have the disease.Experience has shown that this test reveals that 99% of people withthe disease have the disease. The test also reveals that 95% ofpeople who do not have the disease haven’t the disease. If the testreveals the presence of the disease what is the actual probabilitythat the patient has the disease?