The total number of tickets in the lottery is 50, numbered from 1 to 50. We need to find the odds in favor that none of the tickets drawn has a prime number.

Prime numbers are numbers that are divisible only by 1 and themselves. So, the prime numbers between 1 and 50 are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, and 47.

To find the odds in favor, we need to find the number of favorable outcomes and the number of possible outcomes.

Number of favorable outcomes:
In this case, the favorable outcomes are the tickets that do not have a prime number. So, we need to find the number of tickets that are not prime, which is the total number of tickets minus the number of prime tickets.

Number of prime tickets = 15 (as there are 15 prime numbers between 1 and 50)
Total number of tickets = 50

Number of favorable outcomes = 50 - 15 = 35

Number of possible outcomes:
The number of possible outcomes is the total number of ways in which two tickets can be drawn from the 50 tickets. This can be calculated using the combination formula.

Number of possible outcomes = C(50, 2) = 50! / (2! * (50-2)!) = (50 * 49) / (2 * 1) = 1225

Calculating the odds:
The odds in favor are given by the ratio of the number of favorable outcomes to the number of possible outcomes.

Odds in favor = Number of favorable outcomes / Number of possible outcomes
= 35 / 1225
= 17 / 595

Simplifying the ratio by dividing both numerator and denominator by the greatest common divisor, we get:

Odds in favor = 17 / 595 = 1 / 35

To express this ratio in the form of "A:B", we multiply both the numerator and denominator by 18:

Odds in favor = (1 * 18) / (35 * 18) = 18 / 630

Simplifying the ratio by dividing both numerator and denominator by the greatest common divisor, we get:

Odds in favor = 18 / 630 = 1 / 35

So, the odds in favor that none of the tickets has a prime number are 1:35, which is equivalent to option E: 17:18.