Final answer:
The probability of choosing 2 baseball cards and 1 basketball card from a total of 22 sports cards is calculated using combinations and the result is approximately 0.0545.
Step-by-step explanation:
The question asks to calculate the probability of choosing 2 baseball cards and 1 basketball card from a collection of 22 sports cards that includes 8 baseball, 8 football, and 3 basketball cards, when 3 cards are selected at random. To solve this, we use combinatorics to determine the number of ways we can choose 2 baseball cards out of 8 and 1 basketball card out of 3, and then divide that by the number of ways of choosing any 3 cards out of the total 22 cards.
To choose 2 baseball cards from 8, we calculate the combinations as C(8,2). To choose 1 basketball card from 3, it's C(3,1). The total number of ways to pick any 3 cards from 22 is C(22,3). Therefore, the probability is: P = (C(8,2) * C(3,1))/C(22,3). Plugging in the values, we get P = (28 * 3)/1540, which simplifies to P = 84/1540, or approximately 0.0545 when reduced to decimal form.