A hacker has a 1% chance of guessing a password correctly on the first try. If the password is not guessed correctly, the probability drops to 0.1% for the second try. What is the probability the hacker will guess the password within two tries?
Question
A hacker has a 1% chance of guessing a password correctly on the first try. If the password is not guessed correctly, the probability drops to 0.1% for the second try. What is the probability the hacker will guess the password within two tries?
Solution
To find the probability that the hacker will guess the password within two tries, we can calculate the probability of two scenarios:
- The hacker guesses the password correctly on the first try.
- The hacker does not guess the password correctly on the first try, but guesses it correctly on the second try.
Let's calculate the probability for each scenario:
-
The probability that the hacker guesses the password correctly on the first try is 1% or 0.01.
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The probability that the hacker does not guess the password correctly on the first try is 99% or 0.99. The probability that the hacker guesses the password correctly on the second try is 0.1% or 0.001.
To find the probability of scenario 2, we multiply the probability of not guessing correctly on the first try (0.99) by the probability of guessing correctly on the second try (0.001). This gives us 0.99 * 0.001 = 0.00099.
Finally, to find the overall probability of the hacker guessing the password within two tries, we add the probabilities of scenario 1 and scenario 2: 0.01 + 0.00099 = 0.01099.
Therefore, the probability that the hacker will guess the password within two tries is approximately 0.01099 or 1.099%.
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