Question

A team of medical students doing their internship have to assist during surgeries at a city hospital. The probabilities of surgeries rated as very complex, complex, routine, simple or very simple are respectively, 0.15, 0.20, 0.31, 0.26, .08. Find the probabilities that a particular surgery will be rated neither very complex nor very simple 

Answer 1

Let E₁, E₂, E₃, E₄ and E₅ be the events that the surgeries are rated as very complex, complex, routine, simple and very simple respectively.

∴ P(E₁) = 0.15

P(E₂) = 0.20

P(E₃) = 0.31

P(E₄) = 0.26

And P(E₅) = 0.08

P(neither very complex nor very simple) = P(E'₁ ∩ E'₅)

= P(E₁ ∪ E₅)' = 1 – P(E₁ ∪ E₅)

= 1 – [P(E₁) + P(E₅)]

= 1 – [0.15 + 0.08]

= 1 – 0.23

= 0.77