Please help to explain into details. Thank you so much for helping. A bag holds 30 marbles labelled with the numbers 1 to 30. A marble is selected from the bag at random. Let A be the event that the number on the chosen marble is divisible by 2. Let B be the event that the number on the chosen marble is divisible by 3. Let C be the event that the number on the chosen marble is divisible by 4. Let D be the event that the number on the chosen marble is divisible by 10. (a) Are the events A and B independent? Prove it or explain why not. (b) Are the events A and C independent? Prove it or explain why not. (c) Are the events B and D independent? Prove it or explain why not. (d) Are the events C and D independent? Prove it or explain why not.
Please help to explain into details. Thank you so much for helping.
A bag holds 30 marbles labelled with the numbers 1 to 30. A marble is selected from the bag at random. Let A be
the
marble is divisible by 3. Let C be the event that the number on the chosen marble is divisible by 4. Let D be the
event that the number on the chosen marble is divisible by 10.
(a) Are the events A and B independent? Prove it or explain why not.
(b) Are the events A and C independent? Prove it or explain why not.
(c) Are the events B and D independent? Prove it or explain why not.
(d) Are the events C and D independent? Prove it or explain why not.
In this probabilistic inquiry, we delve into the relationships between four distinct events, A, B, C, and D, each representing the divisibility of a randomly selected marble number from 1 to 30 by specific integers. We rigorously examine whether these events are independent or not, employing the fundamental principles of probability to ascertain the degree of interdependence among them.
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