If the score of a hockey game ended at $6$-$4$. Each team with the same equal probability of scoring the next goal. What is the probability that the winning team was never behind for more than one goal?
How would one do this problem?
2026-03-25 09:24:01.1774430641
Hockey game score probability question
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HINT
If you want the total no. of options to be ${10 \choose 6}$, then you are adopting a probability model where e.g. each team scores the next goal with equal probability, and you condition on the final result being $6-4$. This is a perfectly natural model but it is still a conscious choice not explicitly specified in your question.
In this model, each goal sequence is a 10-character string with 6 Ws and 4 Ls, e.g. WWLWLWWWLL. These are the ${10\choose 6}$ strings in your denominator. You can then simply count the strings which fail your criterion. Any string failing your criterion must reach $0-2$ or $1-3$ or $2-4$ at some point. So they are: any strings starting with LL, or LWLL, or WLLL, or WWLLLL, or WLWLLL, or WLLWLL, or LWWLLL, or LWLWLL. I think those are all.