what is the probability that that one of my two picks is selected in NY State's Take 5 - (5) numbers are selected from a set of 39 without replacement
To find the probability that at least one of your two picks is selected in NY State's Take 5 game, you can use the concept of complementary probability.
First, calculate the probability that neither of your picks is selected.
The total number of possible outcomes in which 5 numbers are selected from a set of 39 without replacement is given by the binomial coefficient, which is denoted as C(n, k). In this case, n = 39 (the total number of numbers in the set) and k = 5 (the number of numbers drawn). So, C(39, 5) represents the total number of possible outcomes.
The number of outcomes in which none of your picks is selected can be calculated as C(37, 5) since there are 37 remaining numbers in the set after excluding your two picks.
Therefore, the probability of neither of your picks being selected is:
P(neither pick selected) = C(37, 5) / C(39, 5)
To find the probability that at least one of your two picks is selected, subtract the probability mentioned above from 1 (since 1 - P(neither pick selected) = P(at least one pick selected)):
P(at least one pick selected) = 1 - P(neither pick selected)
Now you can substitute the values into the formula and calculate the probability.