Ask a New Question
Menu

A number cube is rolled three times. An outcome is represented by a string of the sort OEE (meaning an odd number on the first roll, an even number on the second roll, and an even number on the third roll). The outcomes are listed in the table below. Note that each outcome has the same probability.

For each of the three events in the table, check the outcome(s) that are contained in the event. Then, in the last column, enter the probability of the event.

Outcomes Probability
EOE EEO OOE OEE OOO EOO EEE OEO
Event A: An even number on both the first and the last rolls
Event B: Two or more odd numbers
Event C: An even number on the second roll

2 answers

To analyze the events and their outcomes based on rolling a number cube (1 to 6) three times, we can first identify the outcomes specified in your table. Then we can check which outcomes fall into each event category and calculate the associated probabilities.

Here’s the breakdown of the events and their corresponding outcomes:

Outcomes:

  • EOO (Odd first, Even second, Odd third)
  • EEO (Even first, Even second, Odd third)
  • OOE (Odd first, Odd second, Even third)
  • OEE (Odd first, Even second, Even third)
  • OOO (Odd first, Odd second, Odd third)
  • EEO (Even first, Even second, Odd third)
  • EEE (Even first, Even second, Even third)
  • OEO (Odd first, Even second, Odd third)

Total outcomes listed: 8.

Event Definitions:

  1. Event A: An even number on both the first and the last rolls.
  2. Event B: Two or more odd numbers.
  3. Event C: An even number on the second roll.

Outcome Analysis:

  1. Event A - An even number on both the first and the last rolls:

    • Valid Outcomes: EEO, EEE.
    • Outcomes: EEO, EEE.
    • Count: 2

  2. Event B - Two or more odd numbers:

    • Valid Outcomes: OOO, OOE, OEE, OEO, EOO.
    • Outcomes: OOO, OOE, OEE, OEO, EOO.
    • Count: 5

  3. Event C - An even number on the second roll:

    • Valid Outcomes: EOO, EEO, OEE, EEE, OEO.
    • Outcomes: EOO, EEO, OEE, EEE, OEO.
    • Count: 5

Calculation of Probabilities:

  • Total outcomes = 8
  • Probability of an event = (Number of favorable outcomes) / (Total Outcomes)

Probability Table:

| Event | Outcomes | Probability | |-----------|-----------------------------|-------------| | Event A | EEO, EEE | 2/8 = 1/4 | | Event B | OOO, OOE, OEE, OEO, EOO | 5/8 | | Event C | EOO, EEO, OEE, EEE, OEO | 5/8 |

Final outcomes and probabilities can be summarized as follows:

  • Event A: Outcomes EEO, EEE, with probability 1/4.
  • Event B: Outcomes OOO, OOE, OEE, OEO, EOO, with probability 5/8.
  • Event C: Outcomes EOO, EEO, OEE, EEE, OEO, with probability 5/8.

Feel free to ask if you need more clarifications!

wrong