Question

fill in the blank 1 point
the access code to a houses security system consists of four digits.
how many different codes are available if the first digit cannot be 0 and no digit can be repeated?
type your answer...
45 fill in the blank 1 point
the sum of the probabilities of every possible outcome in a probability experiment is always 1. the probability distribution below list the probabilities of every possible outcome in a particular probability experiment.
determine the missing probability value for the probability distribution.

Explanation:

Step1: Analyze the first digit

The first digit cannot be 0, so there are 9 choices (1 - 9).

Step2: Analyze the second digit

Since no digit can be repeated, after choosing the first digit, there are 9 remaining digits (0 and the 8 non - chosen non - zero digits).

Step3: Analyze the third digit

After choosing the first two digits, there are 8 remaining digits.

Step4: Analyze the fourth digit

After choosing the first three digits, there are 7 remaining digits.

Step5: Calculate the total number of codes

Using the multiplication principle, the total number of codes is \(9\times9\times8\times7\).

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for the probability problem:

Step1: Use the property of probability distribution

The sum of all probabilities \(P(x)\) in a probability distribution is 1. Let the missing probability be \(p\).
We know that \(0.05 + p+0.23 + 0.21+0.17 + 0.11+0.01=1\)

Step2: Solve for \(p\)

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Answer:

4536