The estimated probability that it will take at least four patients to find one who is not an elderly patient is 0.1504.
How to calculate the probability?
The number of patients = 10
Elderly patients = 60%
Non-elderly patients = 100% - 60% = 40%
The probability that the first four patients are elderly will be:
= [0.6^0 × (0.4)^10] + [0.6 × (-0.6)^9] + [0.6² × (1 - 0.6)^8] + [0.6³ × (1 - 0.6)^7
= 0.000105 + 0.0016 + 0.01062 + 0.0425
= 0.1504
The probability that exactly two of three randomly selected morning appointments are with elderly patients will be:
= 0.6² × (1 - 0.6)¹.
= 0.432
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