A fair 2
A fair die is thrown two times. What is the probability that the sum of the score is almost 8?
Correct answer:
Showing 2 comments:
Math student
By "almost 8", did you mean "at most 8"?
It's appropriate, in your solution, to double the number of ways to get a total of at most 8 on different outcomes, but it's not appropriate to double the number of times you roll doubles (so 1+1, 2+2, 3+3, 4+4). Therefore, your 30/36 figure over-counts by 4. The correct answer is 26/36. Another way to reach this is to look at a 6-by-6 grid of ordered pairs: (1,1) through (6,6). Diagonals have a constant sum: 1 way to roll 2, 2 ways to roll 3, ..., 6 ways to roll 7, 5 ways to roll 8. Answer: (1+2+3+4+5+6+5)/36=26/36.
It's appropriate, in your solution, to double the number of ways to get a total of at most 8 on different outcomes, but it's not appropriate to double the number of times you roll doubles (so 1+1, 2+2, 3+3, 4+4). Therefore, your 30/36 figure over-counts by 4. The correct answer is 26/36. Another way to reach this is to look at a 6-by-6 grid of ordered pairs: (1,1) through (6,6). Diagonals have a constant sum: 1 way to roll 2, 2 ways to roll 3, ..., 6 ways to roll 7, 5 ways to roll 8. Answer: (1+2+3+4+5+6+5)/36=26/36.
1 year ago 3 Likes
Tips for related online calculators
Would you like to compute the count of combinations?
You need to know the following knowledge to solve this word math problem:
Grade of the word problem:
Related math problems and questions:
- Richard
Richard is conducting an experiment. Every time he flips a fair two-sided coin, he also rolls a six-sided die. What is the probability that the coin will land on tails and the die will land on an even number? - Sum 10
What is the probability that two dice thrown twice in a row will result in the sum of 10? - Probability 71784
What is the probability that if you roll the die twice, the sum of 12 will fall? - Probability 2386
We throw a die seven times. What is the probability that: a) the first, second, and third times fall six and not in all the others, b) 5 does not fall four times in a row, and yes, in the last 3 hours?
- Three dice
The player throwing the three dice asked G. Galilei: "Should I bet on the sum of 11 or the sum of 12?" What did Galilei answer him? Hint: write down all three triples of numbers that can be thrown, have a total of 11, have a total of 12, and compare proba - A six-sided
A six-sided die is rolled once. What is the probability that the number rolled is an even number greater than two? - Dice and coin
A number cube is rolled, and a coin is tossed. The number cube and the coin are fair. What is the probability that the number rolled is greater than two and the coin toss is head?
