SOLUTION: A document is signed with an ElGamal signature. The probability that a signature is forged is (.1). Find the probability that at least one of the three Rob�s signatures is forged.

Question 1088948: A document is signed with an ElGamal signature. The probability that a signature is forged is (.1). Find the probability that at least one of the three Rob�s signatures is forged.
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
we can use the binomial probability distribution
:
Probability (P) (k successes out of n trials) = nCk * p^k * (1-p)^(n-k)
:
Note that nCk = n! / (k! * (n-k)!), p = 0.1, n = 3
:
P (at least one of the 3 signatures is forged) = 1 - P(k=0 out of 3 trials)
:
P(k=0 out of 3 trials) = 3C0 * (0.1)^0 * (1-0.1)^(3-0) = 0.729
:
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P (at least one of the 3 signatures is forged) = 1 - 0.729 = 0.271
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