Is Alex correct in saying that if he rolls an odd number on the first number cube, it is more likely that he will roll an even number on the second number cube? Explain.
Answer (3)
As long as they have the same number of sides, no. The outcome of the first roll does not affect the outcome of the second roll in any way for this situation.
Alex's assumption is incorrect.
No, Alex is not correct. The probability of rolling an even number on a fair six-sided die is independent of the result of the first roll. The result of rolling the first die does not affect the probabilities of rolling numbers on the second die. Each die roll is an independent event.
There are six faces on a standard die, half of which are odd (1, 3, 5) and the other half are even (2, 4, 6), making the probability of rolling an odd or an even number equal to 1/2 or 50%. Therefore, the probability of rolling an even number on the second die is still 1/2, regardless of what the first die roll is. This concept is a fundamental rule in probability known as the independence of events.
The probability of rolling an even or odd number on a single die is an example of a simple probability. Simple probabilities are based on a single event with a certain number of equally likely outcomes.
Alex is incorrect in saying that rolling an odd number on the first cube makes it more likely to roll an even number on the second cube. The outcomes of each roll are independent, and the probability of rolling an even number on the second die remains the same regardless of the first roll. Each die has an equal chance for each face, making the probability 1/2 for even numbers on the second roll.
;
