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) :
[tex]^{10}P_4=\dfrac{10!}{4!(10-4)!}\\\\=\dfrac{10!}{4!6!}=210[/tex]
If we take only odd numbers then the number of ways to make security alarm will be (without repetition):
[tex]^5P_4=\dfrac{5!}{4!(5-4)!}=5[/tex]
Now, the probability that the code only contains odd numbers will be
[tex]P(odd)=\dfrac{5}{210}=0.023809523809\approx0.002381[/tex]
