Let’s analyze the table to understand the situation and verify why Event C is incorrect, based on the problem’s criteria.

Problem Recap:

• A number cube is rolled three times.
• Each outcome is represented by a string of "O" (odd) and "E" (even) depending on whether the number rolled is odd or even.
• There are 8 possible outcomes, each with equal probability.

The outcomes listed are:

• OOE, EEE, EOE, EOO, OEO, OEE, EEO, OOO.

You are tasked with determining the probability for three events:

1. Event A: No even numbers on the last two rolls.

   • The condition is that the second and third rolls should both be odd (O).
   • Outcomes matching this condition: EOO, OOO.
   • Probability = 2 outcomes / 8 total outcomes = 0.25.

2. Event B: More even numbers than odd numbers.

   • This means at least 2 even numbers in the outcome.
   • Matching outcomes: EEE, EOE, OEE, EEO.
   • Probability = 4 outcomes / 8 total outcomes = 0.50.

3. Event C: An even number on the first roll or the third roll (or both).

   • You need to select outcomes where the first or third number is an "E" (even).
   • Let's review the outcomes:
     • OOE (even on the third roll, check).
     • EEE (even on both first and third rolls, check).
     • EOE (even on the first and third rolls, check).
     • EOO (even on the first roll, check).
     • OEO (even on the third roll, check).
     • OEE (even on both second and third rolls, check).
     • EEO (even on both first and second rolls, check).
     • OOO (no evens on first or third rolls, no check).
   • Correct outcomes: OOE, EEE, EOE, EOO, OEO, OEE, EEO.
   • Probability = 7 outcomes / 8 total outcomes = 0.875 (not 0.625).

Your answer of 0.625 was marked incorrect because the correct probability for Event C should be 0.875, as 7 out of the 8 outcomes meet the condition for an even number on the first or third roll.

Would you like further clarification on any part of this?

Related Questions:

1. How would the probability change for Event A if the condition were no odd numbers on the last two rolls?
2. What is the probability of getting exactly two odd numbers in the three rolls?
3. How many outcomes would there be if the die were rolled four times instead of three?
4. If you were to roll the cube twice instead of three times, how would you calculate the probability for similar events?
5. Can you calculate the probability of rolling the same sequence twice in a row in two independent trials of three rolls?

Tip:

When calculating probabilities, always make sure that the number of favorable outcomes is correctly identified based on the specific conditions of the event.