Respuesta :
Answer:
Probability = 0.2381
Step-by-step explanation:
A security alarm requires a four digit code by using 0 - 9 and the digits cannot be repeated.
First we calculate how many codes can be made.
Combination = [tex]^{n}p_{r}[/tex]
Where n = 10 and r = 4
[tex]^{n}p_{r}[/tex] = [tex]\frac{10!}{(10-4)!}[/tex]
= [tex]\frac{10!}{6!}[/tex]
= 10 × 9 × 8 × 7
= 5,040 combinations.
Now we have to find the probability that the code contains only odd numbers. So in 0-9 the odd numbers are = 1, 3, 5, 7, 9
There are 5 odd numbers and we have to make a code of 4 numbers.
Therefore, On first place there are 5 options and in second place 4 options, in third place there are 3 options and in fourth place we have only 2 options.
5 × 4 × 3 × 2 = 120 combinations.
Total combinations of odd numbers are 120.
Then the probability that the code contains only odd numbers is
[tex]p=\frac{120}{5040}[/tex] = 0.0238095 ≈ 0.02381
Probability = 0.2381
