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Answer:
The probability that there is at least one pair but not a three of a kind is 0.6944.
Step-by-step explanation:
We have the case when we have five dices and we roll them and we need that there is at least one pair but not a three of a king which is Two dice showing the same value, but no three dice showing the value.
Total no of outcomes =
We will consider the other cases and then subtract them from the total outcomes.
No of outcomes of 5 of a kind = 6
No of outcomes 4 of a kind and 1 different = (6*5)*5 = 150
No of outcomes with 3 of a kind and 1 different pairs = (6*1*1*5*1)*5C2= 300
No of outcomes with 3 of a kind and two different = 6*5*4*10= 120*10=1200
No of outcomes when all are different = 6! = 720
These all the cases when subtracted from the total will represent the total cases in which there are two dice showing the same value.
Total cases = 6+150+300+1200+720
= 2376
Required no of outcomes = 7776-2376 = 5400
Probability = = 0.6944
Therefore the probability for the case of at least one pair but not a three of a kind is 0.6944.