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If you roll two fair six-sided dice, what is the probability that both dice show an odd number?
Full solution
Q. If you roll two fair six-sided dice, what is the probability that both dice show an odd number?
- Identify Odd Outcomes: First, figure out the number of odd outcomes on one die. Odd numbers on a die are , , and .
- Calculate Probability of Odd Number on One Die: So, there are odd outcomes out of total outcomes on one die. The probability of rolling an odd number on one die is , which simplifies to .
- Multiply Probabilities for Combined Probability: Now, since the two dice are independent, multiply the probabilities of each die to get the combined probability. So, .
- Correct Calculation: But wait, I made a mistake. The probability of rolling an odd number on one die is actually , which doesn't simplify to , it simplifies to . So the correct calculation should be .
