# What is the probability of winning a lottery game where the winning number is made  up of seven digits from 0 to 9 chosen at random?

hala718 | High School Teacher | (Level 1) Educator Emeritus

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The probability of winning the lottery = the probability of choosing all 7 digits correctly. That is:

The probability of choosing the first digit = 1/10

The probability of choosing the 2nd digit = 1/10

The probability of choosing the 3rd digit= 1/10

The proabability of choosing the 4th digit= 1/10

The probability of choosing the 5th digit= 1/10

The probability of choosing the 6th digit= 1/10

The probability of choosing the 7th digit= 1/10

Thne the probability of choosing all 7 digits= 1/10*1/10*1/10*1/10*1/10*1/10*1/10= 1/10^7 = 1/10000000

Then the probability of winning  is one in a 10,000,000

neela | High School Teacher | (Level 3) Valedictorian

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Question: What is the probability of winning a lottery game where winning number is made up of seven digits from 0 to 9 chosen at random:

Each digit could be from 0 to 9 . That is in 10 ways.

The number of ways the 7 digit number could be formed with digits from 0 to 9 is  10*10*10*10*10*10*10 = 10^7. Or the numbers could be any number from  the lowest , 0000000   to  the greatest 9999999  which is 10000000 =10^7.

Therefore getting a particular number for winning has the chance = 1/10000000  = 1/10^7 = 0.0000001.

Hope this helps.