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  $0.3439$ .

Step-by-step 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 = $\frac{9^4}{10^4}$

⇒ Probability of Number without 7 = $\frac{6561}{10000}$

⇒ 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  $0.3439$ .