The population consists of healthy, ill and hospitalized people. A healthy person remains helthy with probability 0.7 or becomes ill with probability 0.3. An ill person recovers with probability 0.6 or becomes hospitalized with probability 0.4. A hospitalized person may recover with probability 0.5 or remain hospitalized with probability 0.5. Find the number of healthy, ill and hospitalized people after a long run of the illness assuming that initially the number of healthy, ill and hospitalized people is: A) v→A=⟨Healthy, ill, hospitalized⟩=⟨h, i, o ⟩=⟨50, 25, 12⟩ B) v→B=⟨Healthy, ill, hospitalized⟩=⟨h, i, o⟩=⟨87, 0, 0⟩

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The population consists of healthy, ill and hospitalized people. A healthy person remains helthy with probability 0.7 or becomes ill with probability 0.3. An ill person recovers with probability 0.6 or becomes hospitalized with probability 0.4. A hospitalized person may recover with probability 0.5 or remain hospitalized with probability 0.5. Find the number of healthy, ill and hospitalized people after a long run of the illness assuming that initially the number of healthy, ill and hospitalized people is:  A) v→A=⟨Healthy, ill, hospitalized⟩=⟨h, i, o ⟩=⟨50, 25, 12⟩  B) v→B=⟨Healthy, ill, hospitalized⟩=⟨h, i, o⟩=⟨87, 0, 0⟩

Sharolyn Larson · Accepted Answer

Introduction:  Given:  Healthy person:  probability of remains healthy =0.7  probability of become ill =0.3  Ill person:  Probability of recovery =0.6  Probability of become hospitalized =0.4  Hospitalized person:  Probability of recovery =0.5  Probability of become hospitalized =0.5  Initial number of healthy, ill, hospitalized people is:  A) v→A=⟨Healthy, ill, hospitalized⟩=⟨h, i, o ⟩=⟨50, 25, 12⟩  B) v→B=⟨Healthy, ill, hospitalized⟩=⟨h, i, o⟩=⟨87, 0, 0⟩  Calculation:  A) v→A=⟨Healthy, ill, hospitalized⟩=⟨h, i, o ⟩=⟨50, 25, 12⟩  Probability of healthy people becomes ill  P=nHealthy people becomes ill)nHealthy people)  0.3=n(H1)50  n(H1)=15  So, 50−15=35  Probability of Ill people become hospitalized =0.4  P=n(ill people becomes hospitalized)n(ill people)  0.4=n(II)25  n(II)=10  So, 25−10=15  Probability of Hospitalized people become hospitalized =0.5  P=n(Hospitalized people becomes hospitalized)n(Ho spitalized people)  0.5=n(Oi)12  n(OI)=6  So, 12−6=6  Number of healthy, ill, hospitalized people after long run of illness =35+15+6=56  B) v→B=⟨Healthy, ill, Hospitalized⟩=⟨h, i, o⟩=⟨87, 0, 0⟩  Probability of healthy people becomes ill  P=n(Healthy people becomes ill)n(Healthy people)  0.3=n(HI)80  n(HI)=24  So, 80−24=56  Number of healthy, ill, hospitalized people after long run of illness =56  Therefore,   A) Number of healthy, ill, hospitalized people after long run of illness =56   B) Number of healthy, ill, hospitalized people after long run of illness =56

The population consists of healthy, ill and hospitalized people. A hea

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