Probability question with dice

In summary, the probability of the first die being a perfect square and the second die being a 4 when two dice are rolled is 1/18. This is calculated by multiplying the individual probabilities of each event occurring (2/6 for a perfect square and 1/6 for a 4). The answer of 3/6 is incorrect because it assumes the dice are being rolled in a specific order, whereas the question does not specify which die should be a perfect square and which should be a 4.
  • #1
nesan
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Two dice are rolled. What is the probability that the first die is a perfect square and the second die is a 4?


First die : 2/6

Second die : 1/6

Won't the probability be just (2/ 6) * (1 / 6) = 2 / 36 = 1 / 18

My answer says 3 / 6 but aren't these events not mutually exclusive? :|
 
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  • #2
The wording is critical. If the question actually reads "that one is a four and the other a perfect square" then the answer is 3/36. This is because the order doesn't matter now, so the possible rolls are 1, 4; 4, 1; 4, 4. As soon as you discriminate the dice as first, second, it collapses to 2/36.
 
  • #3
nesan said:
Two dice are rolled. What is the probability that the first die is a perfect square and the second die is a 4?


First die : 2/6

Second die : 1/6

Won't the probability be just (2/ 6) * (1 / 6) = 2 / 36 = 1 / 18

My answer says 3 / 6 but aren't these events not mutually exclusive? :|

Hi,

The sample space for your question is S={(i,j), i=1,..,6 j=1,...,6} and supposing that the dice are fair, all 36 outcomes have probability 1/36 of occurring.

E is the event: the first dice is a perfect square and the second is a 4.

E={(1,4),(4,4)}.

So P(E)=2/36=1/18 and not 1/2.

If we think about it, if we roll the dice let's say 100 times, we would not expect to get a perfect square for the first dice together with a 4 for the second dice around 50 times.

Does your question involve conditional probability?
 

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

The probability of rolling a specific number on a single dice is 1/6, or 16.67%. This is because there are six possible outcomes (numbers 1-6) and each outcome has an equal chance of occurring.

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

The probability of rolling a certain total on two dice depends on the total. For example, the probability of rolling a total of 7 is 1/6, or 16.67%, because there are 6 ways to roll a 7 (1+6, 2+5, 3+4, 4+3, 5+2, 6+1) out of 36 possible outcomes (6x6). However, the probability of rolling a total of 2 is only 1/36, or 2.78%, because there is only one way to roll a 2 (1+1) out of 36 possible outcomes.

3. What is the probability of rolling a certain sequence on multiple dice?

The probability of rolling a certain sequence on multiple dice depends on the number of dice and the sequence itself. For example, the probability of rolling a sequence of 3-4-5 on three dice is 1/216, or 0.46%, because there is only one way to roll that specific sequence (3 on the first dice, 4 on the second dice, and 5 on the third dice) out of 216 possible outcomes (6x6x6).

4. How can I calculate the probability of rolling a certain outcome with multiple dice?

To calculate the probability of rolling a certain outcome with multiple dice, you can use the following formula: (Number of ways to get the desired outcome)/(Total number of possible outcomes). For example, if you want to know the probability of rolling a total of 7 on two dice, you would calculate it as (6/36), or 1/6, which is 16.67%.

5. How does the probability of rolling certain outcomes change when using different types of dice?

The probability of rolling certain outcomes can change depending on the type of dice used. For example, if you use a 12-sided dice instead of a 6-sided dice, the probability of rolling any specific number would be 1/12 instead of 1/6. Additionally, the probability of rolling certain totals or sequences may also change depending on the number of sides on the dice and the specific outcomes desired.

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