Question

A security alarm requires a four-digit code. The code can use the digits 0–9 and the digits cannot be repeated. What is the approximate probability that the code only contains odd numbers?
0.0005
0.00099
0.012
0.02381

Answer 1

Answer:  0.02381

Step-by-step explanation:

Given: A security alarm requires a four-digit code. The code can use the digits 0–9 and the digits cannot be repeated.

The total number of ways to make security alarm will be  (without repetition) :

$^{10}P_4=\dfrac{10!}{4!(10-4)!}\\\\=\dfrac{10!}{4!6!}=210$

If we take only odd numbers then the number of ways to make security alarm will be (without repetition):

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

Now, the probability that the code only contains odd numbers will be

$P(odd)=\dfrac{5}{210}=0.023809523809\approx0.002381$

Answer 2

The approximate probability that the code only contains odd numbers is 0.02381.