a security alarm requires a four - digit code. the code can use the digits 0 - 9 and the digits cannot be…

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?\n0.0005\n0.00099\n0.012\n0.02381

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?\n0.0005\n0.00099\n0.012\n0.02381

Answer

Explanation:

Step1: Calculate total number of four - digit codes

The number of permutations of (n) distinct objects taken (r) at a time is given by (P(n,r)=\frac{n!}{(n - r)!}). Here, (n = 10) (digits from (0 - 9)) and (r=4), so the total number of four - digit non - repeating codes is (P(10,4)=\frac{10!}{(10 - 4)!}=\frac{10!}{6!}=10\times9\times8\times7 = 5040).

Step2: Calculate number of four - digit codes with only odd numbers

There are 5 odd numbers ((1,3,5,7,9)). Using the permutation formula with (n = 5) and (r = 4), we get (P(5,4)=\frac{5!}{(5 - 4)!}=\frac{5!}{1!}=5\times4\times3\times2=120).

Step3: Calculate the probability

The probability (P) is the number of favorable outcomes divided by the number of total outcomes. So (P=\frac{120}{5040}\approx0.02381).

Answer:

0.02381