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a security alarm requires a four digit code. the code can use 0-9 and the digits cannot be repeated. what is the approximate probability that the code only contains odd number

User Vasylyna
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2 Answers

4 votes

Answer:3125/6561


Step-by-step explanation: Because there are four digits and the question is asking the odds of have odd numbers, the chances of an odd number between 0-9 is 5. 5 out of 9.

(5/9)^4 gives you 3125/6561 or 48%


User Bjornd
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2 votes

Answer: 0.02381

Explanation:

Given: The number of digits from which a security code is made (0-9) = 10

The number of odd digits (1, 3, 5, 7, 9 )= 5

By using Permutations , the number of ways to make a four digit number such that no digit is repeated :-


^5P_4=(5!)/((5-4)!)\\\\=120

The number total number of ways of making four digit number from the 10 digits such that no digit is repeated:-


^(10)P_4=(10!)/((10-4)!)\\\\=10*9*8*7=5040

The probability that the code only contains odd number is given by :-


\text{P(odd)}=(120)/(5040)=0.0238095238095\approx0.02381

Hence, the approximate probability that the code only contains odd number = 0.02381

User Pasukaru
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