In a hospital, there are 10 nurses and 5 physicians. Seven nurses and two physicians are males.
The sample space can be written in a table form.
Staff Females Males Total
Nurses: (3 , 7, 10)
Physicians: (3, 2, 5)
total :
If a person is selected from the staff, what is the probability that a person is nurse of female?
What is the probability that a person selected is a male or physician?
What is the probability that a person selected is male or female?
What is the probability that a person selected is nurse or physician?
What is the probability that a person selected is a nurse or male?
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Staff Females Males Total
Nurses: 3 7 10
Physicians: 2 3 5
Total: 5 10 15
The probability that a person selected is a nurse of female is:
P(nurse or female) = P(nurse and female)/P(total)
P(nurse and female) = 3/15
P(total) = 15/15
Therefore, P(nurse or female) = (3/15)/(15/15) = 3/15 = 1/5 = 0.2
The probability that a person selected is a male or physician is:
P(male or physician) = P(male) + P(physician) - P(male and physician)
P(male) = 10/15
P(physician) = 5/15
P(male and physician) = 2/15
Therefore, P(male or physician) = (10/15) + (5/15) - (2/15) = 13/15 = 0.87
The probability that a person selected is male or female is:
P(male or female) = P(male) + P(female) - P(male and female)
P(female) = 5/15
P(male and female) = 7/15
Therefore, P(male or female) = (10/15) + (5/15) - (7/15) = 8/15 = 0.53
The probability that a person selected is a nurse or physician is:
P(nurse or physician) = P(nurse) + P(physician) - P(nurse and physician)
P(nurse) = 10/15
P(nurse and physician) = 2/15
Therefore, P(nurse or physician) = (10/15) + (5/15) - (2/15) = 13/15 = 0.87