There are 38 numbers, I pick 7. What are probabilities I win exactly one number, no more and no less.

Is this possible to calculate.

It would be simple to calculate what are the chances I don't win any number, but how can you calculate chances of winning exactly one?

  • $\begingroup$ To be clear, are you saying that you choose 7 numbers between 1 and 38, and there are 7 winning numbers, and there is exactly one match? If so, are repetitions allowed i.e. can you choose (1,1,1,1,1,1,1)? $\endgroup$ – pwerth Jan 16 at 19:30
  • $\begingroup$ @pwerth: yes, 7 numbers between 1 and 38 and no repetions are allowed. If 16 is selected, it's eliminated. $\endgroup$ – Stenga Jan 16 at 19:32

You have chosen $7$ numbers. In order for you to match exactly one number, the winning numbers must include $6$ of the $31$ numbers you did not choose. $$\frac{7\cdot\binom{31}{6}}{\binom{38}{7}}\approx40.839\%$$


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.