Final answer:
To find the probability that a randomly selected person from a hospital ward is either female or a doctor, calculate the number of female nurses and add it to the total number of doctors. The probability is the sum of these two divided by the total number of nurses and doctors, resulting in a 75% chance.
Step-by-step explanation:
The question asks for the probability that a randomly selected person from a hospital ward is either female or a doctor. There are 10 nurses and 6 doctors, and we are given that 4 of the nurses and 3 of the doctors are male. To find the total number of females, we subtract the number of male nurses and male doctors from the totals: 10 - 4 = 6 female nurses, and since all doctors are being considered, there are 6 doctors. We’ll add the number of female nurses to the number of doctors to cover all individuals who are either female or a doctor.
Probability calculation:
- Female or doctor = Female nurses + Doctors (since some doctors can be female, we already have them counted in the female nurses)
- Number of females or doctors = Female nurses (6) + All doctors (6) = 12
- Total individuals = Nurses (10) + Doctors (6) = 16
- Probability (female or doctor) = 12 / 16 = 3 / 4 or 0.75
Therefore, the probability that a randomly selected person is either female or a doctor is 0.75, or 75%.