What is the probability of getting the number 10 in a double drawing of a simple New Year lottery including from 1 to 50?

1. The probability of the A1 event that the number 10 will be drawn in one New Year lottery drawing, which includes numbers from 1 to 50, is equal to:

P (A1) = 1/50.

And the probability of the opposite event A1 ‘is:

P (A1 ‘) = 1 – P (A1) = 1 – 1/50 = 49/50.

2. Since the draws are independent, the probability of the event A2 ‘, which is not lucky in any drawing, is equal to:

P (A2 ‘) = P (A1’) ^ 2 = (49/50) ^ 2.

Accordingly, the probability of event A2, that at least in one drawing the number 10 will be drawn, is equal to:

P (A2) = 1 – P (A2 ‘) = 1 – (49/50) ^ 2 = 99/2500 = 0.0396.

Answer: 0.0396.