A pack of 50 tickets is numbered from 1 to 50 and is shuffled. Two tickets are drawn at random. Find the probability that (i) both the tickets drawn bear prime numbers (ii) Neither of the tickets drawn bear prime numbers.20 cards are numbered from 1 to 20. If one card is drawn at random, what is the probability that number on the card is: 1. Prime number 2. Odd Number 3. A multiple of 54. Not divisible by 3

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1. Probability of both tickets drawn bearing prime numbers: First, let's determine the number of prime numbers between 1 and 50. They are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, and 47, totaling 15 prime numbers. Now, for both tickets to bear prime numbers, we need to calculate the probability of choosing a prime number for the first ticket and then another prime number for the second ticket. Probability of first ticket being prime = Number of prime numbers / Total number of tickets = 15/50. After drawing the first prime number, there are 14 prime numbers left out of 49 tickets. Probability of second ticket being prime = Number of remaining prime numbers / Remaining tickets = 14/49. Therefore, the probability of both tickets being prime = (15/50) * (14/49).

2. Probability of neither ticket bearing prime numbers: This is essentially the complement of the event where both tickets are prime. Probability of neither ticket being prime = 1 - Probability of both tickets being prime.

Moving to the next question about drawing one card from 20:

1. Probability that the number on the card is a prime number: Prime numbers between 1 and 20 are: 2, 3, 5, 7, 11, 13, 17, and 19. So, there are 8 prime numbers out of 20. Probability of drawing a prime number = Number of prime numbers / Total number of cards.

2. Probability that the number on the card is an odd number: Out of 20 cards, there are 10 odd numbers (1, 3, 5, ..., 19). Probability of drawing an odd number = Number of odd numbers / Total number of cards.

3. Probability that the number on the card is a multiple of 5: Multiples of 5 between 1 and 20 are: 5, 10, 15, and 20. So, there are 4 multiples of 5 out of 20. Probability of drawing a multiple of 5 = Number of multiples of 5 / Total number of cards.

4. Probability that the number on the card is not divisible by 3: Numbers not divisible by 3 are: 1, 2, 4, 5, 7, 8, 10, 11, 13, 14, 16, 17, 19, and 20. There are 14 such numbers out of 20. Probability of drawing a number not divisible by 3 = Number of such numbers / Total number of cards.

These calculations will help us understand the likelihood of each event occurring, aiding in solving probability problems effectively. If you need further clarification or assistance, feel free to ask! Remember, UrbanPro is the best platform for online coaching and tuition.