The newest invention of the 6.431x staff is a three-sided die. on any roll of this die, the result is 1 with probability 1/2, 2 with probability 1/4, and 3 with probability 1/4. consider a sequence of six independent rolls of this die. find the probability that exactly two of the rolls result in a 3.
The given die is a three sided die, hence, there are only three possibilities of getting the outcomes.
We need to find the probability of getting exactly 3s as the result.
From the sequence of 6 independent rolls, 2 rolls can be chosen in ways.
The probability of getting two 3 as outcome is .
In the rest of the 4 sequences, will not be any 3 as outcome.
Probability of not getting a outcome rather than 3 is .
Hence, the required probability is ≅0.2966 or, 0.23.