Final answer:
The probabilities are as follows: (i) 1/25 for both cards being multiples of 5, (ii) 2/95 for the first card being an even number and the second card being a prime number, and (iii) 13/20 for neither card being a multiple of 3. Option B is the correct answer.
Step-by-step explanation:
Let's start by calculating each probability step by step:
- Both cards are multiples of 5: There are 4 multiples of 5 within the numbers 1 to 20 (5, 10, 15, and 20). Once one is drawn, there are 3 left, and only 19 cards remain to pick from, so the probability is (4/20) * (3/19) = 1/25.
- The first card is an even number and the second is a prime number: There are 10 even numbers (2, 4, 6, 8, 10, 12, 14, 16, 18, 20) and, excluding 2 (which is even), there are 7 prime numbers left (3, 5, 7, 11, 13, 17, 19). The probability for the first card is 10/20 and for the second card (after drawing an even number), it's 7/19. The combined probability is (10/20) * (7/19) = 7/38 or 2/95 after simplification.
- Neither card is a multiple of 3: Multiples of 3 in the set are 3, 6, 9, 12, 15, and 18; six in total. The probability for the first card is thus 14/20 (since there are 20 - 6 = 14 numbers not multiples of 3) and for the second, it's 13/19. This gives a probability of (14/20) * (13/19) = 91/190 which simplifies to 13/20.
Creating a tree diagram would involve drawing branches for each possibility and labeling them with the calculated probabilities. However, please note that such a visual representation cannot be accurately conveyed in a text-only format.
The correct probabilities are: (i) 1/25, (ii) 2/95, and (iii) 13/20, which corresponds to option B.