How do you calculate the likelihood of drawing certain cards in your opening hand?
The calculation you are looking for is called a Hypergeometric Distribution. This calculated your chances of drawing a particular number of "successes" from a population, without replacement.


Population Size: 60 cards
Successes in Population: 4 Birds of Paradise
Sample Size: 7 cards
Successes in Sample: 1 (the minimum number we want to draw)
Results: 39% chance of drawing at least 1 Birds of Paradise.


In the Hypergeometric Distribution calculator linked above, that result is represented in the Cumulative Probability: P(X &ge; 1) field: the chance of drawing greater than or equal to 1.

The online calculator will also give you the odds of drawing greater than that many successes in the sample (6%, the P(X > 1) result), and exactly that number (33%, the Hypergeometric Probability: P(X = 1) result).

You can see the calculation on the Wikipedia page, or searching math.stackexchange.com for Hypergeometric Distribution. Unfortunately, this site doesn't support math formatting. (Note: You will also need to know how to calculate binomial coefficients (and factorials).