If y has no factor z such that 1 < z < y, then y must be prime. Let's look at a few examples to see why this is true:
6 has a factor 2 such that 1 < 2 < 6: 6 is NOT prime
15 has a factor 5 such that 1 < 5 < 15: 15 is NOT prime
3 has NO factor between 1 and 3: 3 IS prime
7 has NO factor between 1 and 7: 7 IS prime
Because it is selected from Set B, y is a prime number between 10 and 50, inclusive. The only prime number that is divisible by 3 is 3, so y is definitely not divisible by 3.
Thus, xy is only divisible by 3 if x itself is divisible by 3. We can rephrase the question: “What is the probability that a multiple of 3 will be chosen randomly from Set A?”
There are 21 – 10 + 1 = 12 terms in Set A. Of these, 4 terms (12, 15, 18, and 21) are divisible by 3.
There are 21 – 10 + 1 = 12 terms in Set A. Of these, 4 terms (12, 15, 18, and 21) are divisible by 3.
Thus, the probability that x is divisible by 3 is :- 4/12 = 1/3
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Thanks & Regards,
Anaira Mitch