A survey conducted on a group of patients showed that these patients either have a heart disease only of a lung disease only or both diseases. It was noted that: • 60 % of the patients are men. • Among the men: 20 % have a heart disease only and 50% have a lung disease only. Among the women: 25% have a heart disease only and 40% have both diseases. One patient is selected at random. Consider the following events: • M: "The selected patient is a men"; • H: "The selected patient has a heart disease only" • L: "The selected patient has a lung disease only"; • B: "The selected patient has both diseases". Part A 1) Calculate the probabilities P(MOH), P(MOL) and P(MOB). 2) Calculate P(H), P(L) and verify that P(B) 0.34. 33 3) Show that P(HUL)= 50 4) Knowing that the selected patient has only one disease, calculate the probability that this patient has a heart disease. Part R
A survey conducted on a group of patients showed that these patients either have a heart disease only of a lung disease only or both diseases. It was noted that: • 60 % of the patients are men. • Among the men: 20 % have a heart disease only and 50% have a lung disease only. Among the women: 25% have a heart disease only and 40% have both diseases. One patient is selected at random. Consider the following events: • M: "The selected patient is a men"; • H: "The selected patient has a heart disease only" • L: "The selected patient has a lung disease only"; • B: "The selected patient has both diseases". Part A 1) Calculate the probabilities P(MOH), P(MOL) and P(MOB). 2) Calculate P(H), P(L) and verify that P(B) 0.34. 33 3) Show that P(HUL)= 50 4) Knowing that the selected patient has only one disease, calculate the probability that this patient has a heart disease. Part R
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Part A number 4 please
Transcribed Image Text:A survey conducted on a group of patients showed that these patients either have a heart disease only or a
lung disease only or both diseases. It was noted that:
• 60 % of the patients are men.
• Among the men: 20 % have a heart disease only and 50% have a lung disease only.
• Among the women: 25% have a heart disease only and 40% have both diseases.
One patient is selected at random.
Consider the following events:
• M: "The selected patient is a men";
• H: "The selected patient has a heart disease only"
• L: "The selected patient has a lung disease only";
• B: "The selected patient has both diseases".
Part A
1) Calculate the probabilities P(MnH),P(MOL) and P(MoB).
2) Calculate P(H), P(L) and verify that P(B) =0.34.
33
3) Show that P(HUL)=-
50
4) Knowing that the selected patient has only one disease, calculate the probability that this patient has
a heart disease.
Part B
The group consists of 500 patients. The names of three patients were randomly and simultaneously
selected to win an insurance policy each.
Knowing that the three selected patients have both diseases, calculate the probability that they are men.
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