QuestionWhat is the probability that a randomly chosen patient was satisfied or had brain surgery? Round to 3 decimal places.

Studdy Solution

STEP 1

Assumptions1. The number of patients who had heart surgery and were satisfied is27. . The number of patients who had heart surgery and were not satisfied is28.
3. The number of patients who had brain surgery and were satisfied is32.
4. The number of patients who had brain surgery and were not satisfied is38.
5. The number of patients who had cosmetic surgery and were satisfied is43.
6. The number of patients who had cosmetic surgery and were not satisfied is48.
7. We are looking for the probability that a patient was either satisfied or had brain surgery.

STEP 2

First, we need to find the total number of patients. We can do this by adding up all the patients in each category.
$Total\, patients = Heart\, satisfied + Heart\, not\, satisfied + Brain\, satisfied + Brain\, not\, satisfied + Cosmetic\, satisfied + Cosmetic\, not\, satisfied$

STEP 3

Now, plug in the given values for each category to calculate the total number of patients.
$Total\, patients =27 +28 +32 +38 +43 +48$

STEP 4

Calculate the total number of patients.
$Total\, patients =27 +28 +32 +38 +43 +48 =216$

STEP 5

Next, we need to find the number of patients who were either satisfied or had brain surgery. This is the sum of the number of satisfied patients and the number of patients who had brain surgery, minus the number of patients who were satisfied and had brain surgery (since they are counted twice).
$atisfied\, or\, Brain\, surgery = Heart\, satisfied + Brain\, satisfied + Cosmetic\, satisfied + Brain\, not\, satisfied - Brain\, satisfied$

STEP 6

Now, plug in the given values for each category to calculate the number of patients who were either satisfied or had brain surgery.
$atisfied\, or\, Brain\, surgery =27 +32 +43 +38 -32$

STEP 7

Calculate the number of patients who were either satisfied or had brain surgery.
$atisfied\, or\, Brain\, surgery =27 +32 +43 +38 -32 =108$

STEP 8

Now that we have the number of patients who were either satisfied or had brain surgery and the total number of patients, we can find the probability that a patient was either satisfied or had brain surgery. This is the number of patients who were either satisfied or had brain surgery divided by the total number of patients.
$Probability =atisfied\, or\, Brain\, surgery / Total\, patients$

STEP 9

Plug in the values for the number of patients who were either satisfied or had brain surgery and the total number of patients to calculate the probability.
$Probability =108 /216$

STEP 10

Calculate the probability, rounding to3 decimal places.
$Probability =108 /216 =0.500$ The probability that a patient was either satisfied or had brain surgery is0.500.

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