Question

if i were to randomly generate a 4-digit number, how likely is it that my number will include at least 1 seven?​

Answer 1

Probability that number will include at least 1 seven is
`0.3439` .

Explanation:

Here we have , if i were to randomly generate a 4-digit number, We need to find how likely is it that my number will include at least 1 seven . Let's find out:

Out of 10 digits ( 0,1,2,3,4,5,6,7,8,9) , We are supposed to find probability to generate a 4 digit number with at least one times 7 . We can find this as Probability for at least one 7 = 1 - Probability for no 7

Total number of combinations =
`10^4`

Total number of combinations without 7 =
`9^4`

Probability of Number without 7 =
`(9^4)/(10^4)`

⇒ Probability of Number without 7 =
`(6561)/(10000)`

⇒ Probability of Number without 7 =
`0.6561`

∴ Probability for at least one 7 = 1 - Probability for no 7

⇒
`1-0.6561`

⇒
`0.3439`

Therefore ,Probability that number will include at least 1 seven is
`0.3439` .