Assuming the results of two patients are independent events, the probability that neither one of them will be successfully cured is 0.04.
The success rate of a medical treatment means the probability the treatment will cure the patient.
Let the two patients are patient A and patient B.
From the problem:
P(A_success) = 0.8
P(B_success) = 0.8
Which means:
P(Afailed) = 1 - 0.8 = 0.2
P(Bfailed) = 1 - 0.8 = 0.2
The probability of two independent events is:
P (A∩B) = P(A) . P(B)
Therefore,
P(Afailed ∩ Bfailed) = P(Afailed) . P(Bfailed)
= 0.2 . 0.2 = 0.04
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