A hospital reports that two patients have been admitted who have contracted Crohn's disease. Suppose our experiment consists of observing whether each patient survives or dies as a result of the disease. The simple events and probabilities of their occurrences are shown in the table (where S in the first position means that patient 1 survives, D in the first position means that patient 1 dies, etc.). $$\begin{array} { c c }
\text { Simple Events } & \text { Probabilities } \
S S & 0.59 \
S D & 0.11 \
D S & 0.10 \
D D & 0.20
\end{array}$$ Find the probability that at least one of the patients does not survive.
A) 0.41
B) 0.21
C) 0.20
D) 0.11

Question

A hospital reports that two patients have been admitted who have contracted Crohn's disease. Suppose our experiment consists of observing whether each patient survives or dies as a result of the disease. The simple events and probabilities of their occurrences are shown in the table (where S in the first position means that patient 1 survives, D in the first position means that patient 1 dies, etc.). $$\begin{array} { c c } 
\text { Simple Events } & \text { Probabilities } \
S S & 0.59 \
S D & 0.11 \
D S & 0.10 \
D D & 0.20
\end{array}$$ Find the probability that at least one of the patients does not survive.
A) 0.41
B) 0.21
C) 0.20
D) 0.11

Quizplus · Accepted Answer

The probability that at least one of the patients does not survive is the complement of the probability that both patients survive. The probability that both patients survive is 0.59, so the probability that at least one of the patients does not survive is 1 - 0.59 = 0.41.