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 contains only odd numbers

Answer 1

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 = $^{n}p_{r}$

Where n = 10 and r = 4

$^{n}p_{r}$ = $\frac{10!}{(10-4)!}$

         = $\frac{10!}{6!}$

         = 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

$p=\frac{120}{5040}$ = 0.0238095 ≈  0.02381

Probability = 0.2381