Question

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

Answer 1

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%

Answer 2

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