What is the Probability of Throwing Two Dice and Getting Specific Numbers?

In summary, the conversation discusses the probability of getting a 2 on one die and a total score greater than 8 when a pair of dice are rolled, given that one die shows a 6. The correct answers are 2/11 and 7/11, respectively. The conversation also mentions using a probability tree, but it is unclear how that would lead to the correct answers. The question may be poorly worded as it is unclear if the die showing a 6 was chosen at random or not.
  • #1
desmond iking
284
2

Homework Statement



A pair of dice are thrown. If a die show number 6 , what is the probability of (a)another die show number 2? (b) total score for both number greater than 8 ?

for part (a) , my working is 1/6 x 1/6 = 1/36

but actual ans is 2/11 for part (b), the ans is 7/11


Homework Equations





The Attempt at a Solution

 
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  • #2
desmond iking said:

Homework Statement



A pair of dice are thrown. If a die show number 6 , what is the probability of (a)another die show number 2? (b) total score for both number greater than 8 ?

for part (a) , my working is 1/6 x 1/6 = 1/36

but actual ans is 2/11 for part (b), the ans is 7/11


Homework Equations





The Attempt at a Solution


Write down all the outcome pairs where at least one die shows a 6. How many such pairs do you have? How many of those pairs also include a 2?
 
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  • #3
(1,6) , (2,6) , (3,6) , (4,6) , (5,6) , (6,6)

one contain (2,6)
 
  • #4
What about (6,1),(6,2) etc.?
 
  • #5
LCKurtz said:
What about (6,1),(6,2) etc.?

hi, i got the solution now. but i just can't understand why i can't use the probability tree to get the ans as the photo below?
 

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  • #6
You drew a tree, but you haven't shown getting an answer to the question using it. What answer do you think the tree is leading you to?
 
  • #7
desmond iking said:
A pair of dice are thrown. If a die show number 6 , what is the probability of (a)another die show number 2?
Is that the exact wording? If so, it's a terrible question. As LCKurtz presumed, it almost certainly intended "if at least one die shows a 6", but that's not what it says.
It all hinges on the basis for selecting the die showing a six. The wording suggests that the observer picked one die at random and saw that it was a six. That will not give 2/11 as the answer.
 

Related to What is the Probability of Throwing Two Dice and Getting Specific Numbers?

1. What is the probability of rolling a specific number on a single die?

The probability of rolling a specific number on a single die is 1/6 or approximately 16.67%. This is because there are six possible outcomes when rolling a die (1, 2, 3, 4, 5, or 6) and each outcome has an equal chance of occurring.

2. What is the probability of rolling a certain number on two dice?

The probability of rolling a certain number on two dice is determined by the number of ways that number can be rolled divided by the total number of possible outcomes. For example, the probability of rolling a 7 on two dice is 1/6 or approximately 16.67% because there are six ways to roll a 7 (1+6, 2+5, 3+4, 4+3, 5+2, or 6+1) out of 36 total outcomes (6 possible outcomes on the first die multiplied by 6 possible outcomes on the second die).

3. What is the probability of rolling a total of 10 on three dice?

The probability of rolling a total of 10 on three dice can be calculated by finding the number of ways to roll a 10 and dividing it by the total number of outcomes. In this case, there are 27 ways to roll a 10 (1+4+5, 1+5+4, 2+3+5, 2+4+4, 2+5+3, 3+2+5, 3+3+4, 3+4+3, 3+5+2, 4+1+5, 4+2+4, 4+3+3, 4+4+2, 4+5+1, 5+1+4, 5+2+3, 5+3+2, 5+4+1, 6+1+3, 6+2+2, 6+3+1, 7+1+2, 7+2+1, 8+1+1, 6+3+1, 7+2+1, 8+1+1, 9+1+0, and 10+0+0) out of 216 total outcomes (6 possible outcomes on the first die multiplied by 6 possible outcomes on the second die multiplied by 6 possible outcomes on the third die).

4. What is the probability of rolling a number higher than 4 on a single die?

The probability of rolling a number higher than 4 on a single die is 2/3 or approximately 66.67%. This is because there are four possible outcomes that are higher than 4 (5, 6, 7, or 8) out of six total outcomes, and each outcome has an equal chance of occurring.

5. How can the probability of rolling dice be used in real life?

The probability of rolling dice can be used in a variety of real-life situations, such as in games of chance like gambling or board games, in statistics to analyze data, and in decision-making processes. For example, a company may use the probability of different outcomes to determine the risk associated with a potential business venture, or a sports team may use the probability of certain plays to strategize during a game.

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