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

Explanation:

Step1: Calculate total 4-digit codes

Total permutations of 10 digits taken 4 at a time: $P(10,4) = 10 \times 9 \times 8 \times 7 = 5040$

Step2: Calculate valid odd-only codes

Odd digits (1,3,5,7,9): 5 total. Permutations of 5 digits taken 4 at a time: $P(5,4) = 5 \times 4 \times 3 \times 2 = 120$

Step3: Compute probability ratio

Probability = $\frac{\text{Valid codes}}{\text{Total codes}} = \frac{120}{5040}$

Step4: Simplify the fraction

$\frac{120}{5040} = \frac{1}{42} \approx 0.02381$

Answer:

0.02381