easy Probability

Lucky Lottery

A release-checked easy problem for training Combinations and Permutations, Hypergeometric.

Question

A lottery has an urn consisting of $70$ balls labeled distinct numbers $1-70$. $6$ balls are drawn at random for a lottery, and your lottery ticket also has $6$ distinct random numbers $1-70$ on it. You win the lottery if either $5$ or $6$ of your numbers match those drawn (in any order). Find the probability of winning the lottery. If the probability you find is $p$, report $p \cdot 10^6$, rounded to the nearest hundredth.

Practice focus

This Probability problem is tagged Combinations and Permutations, Hypergeometric. State the random variables and conditioning information explicitly, then check the result against boundary cases before opening hints or a solution.