Dice are the most commonly used probability tool in games today. The number of sides on the dice and the number of dice used will help determine probability of an event with the use of dice. Suppose two dice are needed for a war game. The dice are rolled together to produce an outcome.

Question

During a game, in order to move onto the next round of play, a player must roll a 7
.

1. What is the probability of rolling a 7
and moving onto the next round of play?

2. What are the odds of rolling a 7
A. Probability 1/6 odds 1:7
B. Probability 1/7 odds 7:36
C. Probability 7/29 odds7:36
D. Probability 6/36 odds 7:12
E. Probability 7/12 odds 1:5
F. Probability 7/12 odds 5:6
G. Probability 1/6 odds 1:5
H. Probability 1/3 odds 21:15
J. Probability 1/3 odds 22:36
Best answer

Answer 1

To calculate the probability of rolling a 7 with two six-sided dice, we first need to determine the total number of possible outcomes when rolling two dice and then the number of ways to get a sum of 7.

1. Total Outcomes: Each die has 6 sides, so when rolling two dice, the total number of outcomes is: \[ 6 \times 6 = 36 \]

2. Favorable Outcomes for Rolling a 7: The pairs of dice that give a sum of 7 are:

   • (1, 6)
   • (2, 5)
   • (3, 4)
   • (4, 3)
   • (5, 2)
   • (6, 1)

   There are 6 favorable outcomes that result in a sum of 7.

3. Probability of Rolling a 7: The probability \( P \) of rolling a 7 is given by: \[ P(7) = \frac{\text{Number of Favorable Outcomes}}{\text{Total Outcomes}} = \frac{6}{36} = \frac{1}{6} \]

4. Odds of Rolling a 7: Odds are calculated as the ratio of the number of favorable outcomes to the number of unfavorable outcomes. The unfavorable outcomes when rolling two dice (not getting a sum of 7) would be the total outcomes minus the favorable outcomes: \[ \text{Unfavorable Outcomes} = 36 - 6 = 30 \]

   Therefore, the odds in favor of rolling a 7 are: \[ \text{Odds}(7) = \text{Favorable Outcomes : Unfavorable Outcomes} = 6 : 30 = 1 : 5 \]

Putting it all together we have:

• Probability of rolling a 7: \( \frac{1}{6} \)
• Odds of rolling a 7: \( 1 : 5 \)

Thus, the best answer choice is: G. Probability 1/6 odds 1:5