Question

Math
Compound probability using a organized list

Answer 1

`\huge\boxed{\sf Probability = (3)/(8) }`

Explanation:

`\displaystyle Probability = (Number \ of \ codes \ with \ 2 \ 0s)/(Total \ number \ of \ codes)`

According to the fundamental principle of counting, to find the total number of codes, we need to multiply the number of options we have for each digits by the number of digits. Hence, we have two options for each digit ( 1 and 0 ) and we have 4 digits. So,

= 2 * 2 * 2 * 2

= 16 possible codes (Total)

Now, Codes with two zeroes:

= 0101,0011,1100,1010,1001,0110 (Maximum number of codes for 2 0s)

Hence, The probability:

Probability = 6 / 16

Probability = 3 / 8

`\rule[225]{225}{2}`

Hope this helped!

~AH1807