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?

a)0.0005
b)0.00099
c)0.012
d)0.02381

Answer 1

d00.02381 is the answer

Answer 2

You have 10 digits: 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, among them there are 5 odd digits: 1, 3, 5, 7, 9.

A security alarm requires a four-digit code with only odd different digits. On the first place of the code could be 1 digit from 5 odd digits, on the second place of the code could be 1 digit from remaining 4 digits, on the third place could be 1 from remaing 3 digits and on the last fourth place could be 1 from remaining 2 odd digits. In total you can create 5·4·3·2=120 different four-digit code with only odd different digits.

In the same way you can count how many different codes you can create from all digits: on the first place of the code could be 1 digit from 10 digits, on the second place of the code could be 1 digit from remaining 9 digits, on the third place could be 1 from remaing 8 digits and on the last fourth place could be 1 from remaining 7 digits. In total you can create 10·9·8·7=5040 different four-digit code with different digits.

Then the probability that the code only contains odd numbers is

`Pr=(120)/(5040)=(1)/(42)\approx 0.02381`.

Answer: correct choice is D.