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? 0.0005 0.00099 0.012 0.02381

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? 0.0005 0.00099 0.012 0.02381

Answer

Explanation:

Step1: Calculate the total number of four - digit codes

The total number of four - digit codes using digits (0 - 9) without repetition is (n(S)=P(10,4)=\frac{10!}{(10 - 4)!}=\frac{10!}{6!}=10\times9\times8\times7 = 5040)

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

There are (5) odd digits ((1,3,5,7,9)). The number of four - digit codes using these (5) odd digits without repetition is (n(A)=P(5,4)=\frac{5!}{(5 - 4)!}=\frac{5!}{1!}=5\times4\times3\times2=120)

Step3: Calculate the probability

The probability (P=\frac{n(A)}{n(S)}=\frac{120}{5040}\approx0.02381)

Answer:

(0.02381)