Final Answer:
a) The probability of drawing a card with a number divisible by 2 or 3 is 2/3.
b) The probability of drawing a card with a perfect square number is 1/5.
c) The probability of drawing a card that is neither divisible by 2 nor 5 is 2/5.
d) The probability of drawing a card with a prime number is 1/5.
Explanation:
To find the probability in each case, we need to determine the favorable outcomes and divide by the total number of possible outcomes.
a) Numbers divisible by 2 or 3: There are 25 numbers divisible by 2 (even numbers) and 16 numbers divisible by 3. However, we need to subtract the numbers divisible by both 2 and 3 (i.e., multiples of 6) to avoid double counting. So, 25 + 16 - 8 = 33 favorable outcomes. The probability is then 33/50, which simplifies to 2/3.
b) Perfect square numbers: There are 7 perfect squares between 1 and 50 (1, 4, 9, 16, 25, 36, 49). The probability is 7/50, which does not simplify further.
c) Numbers neither divisible by 2 nor 5: Numbers divisible by 5 are multiples of 5, and numbers divisible by 2 are even. Therefore, numbers neither divisible by 2 nor 5 are the odd numbers that are not multiples of 5, which are 15 in total. The probability is 15/50, simplified to 3/10.
d) Prime numbers: There are 15 prime numbers between 1 and 50. The probability is 15/50, which simplifies to 3/10.
