I purchased10 football squares for my office pool. How can i calculate the likelihood of winning any one of the four prizes awarded? Each square carries a 1% chance for each quarter of the game, so shouldn't each square have an overall probability of winning any prize of 4%? And what would happen if i purchased 30 squares.......my overall probability couldn't possibly be 120% thanks for any help
I don't know exactly what a "football square" is, but the probabilities don't add up for two non-disjoint events .
$P(A \cup B) \le P(A) + P(B)$ , with equality iff $A \cap B = \phi$
The probability of winning with one square is the complement of losing all four quarters. This is equal to $(1-0.01)^4$ or approximately 0.961. The probability of winning would then be $1-0.961=0.039$, or 3.9%. The probability of winning with $n$ squares is the complement of losing all $n$ squares, or $1-0.961^n$. For 10 squares, this is approximately 0.331, or 33.1%. For 30 squares, this is approximately 0.701, or 70.1%.