I am solving my homework of probability class. I am not sure my approach is correct or not.
The problem consists of three questions:
Throw a pair of dice at the same time.
- If the dice are distinguishable, what is the probability of getting 3 from one die and 4 from another?
- If the dice are not distinguishable, what is the probability of getting 3 from one die and 4 from another?
- If the dice are not distinguishable and the possibility of getting any identical number for the two dice is eliminated, what is the
probability of getting 3 from one die and 4 from another?
For Q1, the sample space is $6*6$ and the cases are (3,4) and (4,3), thus the probability is $2/6^2=1/18$.
For Q2, No matter what the dice are distinguishable or not, the probability of the same event is not changed unless a particular die is specified to have a certain value. So, the probability is the same as Q1. => $1/18$
For Q3, the sample space is $6*5$ and the cases are (3,4) and (4,3), thus the probability is $2/(6*5)=1/15$.
Could you check my solution is going right direction?
Best Answer
you have done it correctly.
Even if two dice are indistinguishable the probability of getting 3 from one die and 4 from another will remain same.
we can not distinguish between (3,4) and (4,3) but it does not affect the fact that they can occur in two different ways.