I have four different tutors in my Commander deck of 100 cards. What are the odds that I will draw at least one of them in my first seven cards drawn for my hand? Back in the day I knew how to do this, but haven't touched statistics in many years.
The easy method is to multiply the probability that each of your starting 7 isn't one of the cards you want, then subtract that total from 1.
Assuming you desire any of the tutors, or the card to be tutored, there are 94 cards that aren't what you want out of the 99 in your deck when you start drawing.
1 - ((94/99) * (93/98) * (92/97) * (91/96) * (90/95) * (89/94) * (88/93))
Questions such as this can be answered with a hypergeometric calculator, since the underlying distribution in mathematics is the hypergeometric distribution.
- Population size = 99 (since there are only 99 cards in a Commander deck, the last card is the Commander in the Command zone)
- Sample size = 7 (your opening hand size)
- Successes in population = 4 (you want to draw the four tutors; if you also include the card to be tutored for then successes in population would be 5)
- Successes in Sample = 1 (you only need one of them in your opening hand)
Chance to draw 1 or more of the wanted card 25.8%
Chance to draw exactly 1 of the wanted card 23.4%
Chance to draw 1 or less of the wanted card 97.6%
Chance to draw 0 of the wanted card 74.2%