1. Arabella's password consists of one letter followed by 2 digits. What is the probability of correctly guessing arabella's password?
2. If the probability of an event happening is p, what is an algebraic expression that represents the probability that the event does not happen?
Number of possible passwords = 26*10*10 = 2600
so p = 1/2600
not p = 1 - p
1. To calculate the probability of correctly guessing Arabella's password, we need to know the number of possible combinations. Since the password consists of one letter followed by 2 digits, we need to determine the number of letters (26 possibilities) and the number of digits (10 possibilities for each digit).
The total number of possibilities is obtained by multiplying the number of choices for each position, which is 26 for the letter and 10 for each digit. Therefore, the total number of possible combinations is 26 * 10 * 10 = 2600.
Since there is only one correct password, the probability of correctly guessing the password is 1/2600 ≈ 0.0004.
2. The probability of an event happening is denoted as p. The probability that the event does not happen can be represented using the algebraic expression (1 - p).
For example, if the probability of an event happening is 0.3, the probability that it does not happen would be (1 - 0.3) = 0.7.
1. To find the probability of correctly guessing Arabella's password, we need to know some additional information. Specifically, we need to know the total number of possible passwords that can be formed using one letter followed by two digits. Let's assume that there are 26 possible letters (A-Z) and 10 possible digits (0-9).
The probability of correctly guessing the first letter is 1 out of 26, since there is only one correct letter out of the 26 options. Similarly, the probabilities of correctly guessing each digit are 1 out of 10.
Since the events (guessing the letter and each digit) are independent, we can multiply the probabilities together to find the overall probability. Therefore, the probability of correctly guessing Arabella's password is:
Probability = (1/26) * (1/10) * (1/10)
Note that we assume there are no restrictions on repeating letters or digits in the password.
2. If the probability of an event happening is p, then the probability of the event not happening can be represented by the expression (1 - p).
This is because the sum of the probabilities of an event happening and not happening is always equal to 1. So, if the probability of an event happening is p, then the probability of the event not happening is (1 - p).
For example, if the probability of rolling a 6 on a fair six-sided die is 1/6, then the probability of not rolling a 6 is (1 - 1/6) = 5/6.