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

Step-by-step 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 :-

$^5P_4=\dfrac{5!}{(5-4)!}\\\\=120$

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

$^{10}P_4=\dfrac{10!}{(10-4)!}\\\\=10\times9\times8\times7=5040$

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

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

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