If 4 dices are rolled in how many ways the largest of them is not 4?

Question

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Answer 1

This is a problem that involves the complement.

 

What is the probability that 4 IS the largest number?

 

You must guarantee a 4 and then the remaining 3 can be any number less than or equal to 4.

You can do this in 4C1*1*4*4*4=256 ways....out of 6⁴  making the probability 16/81.

 

So the probability that 4 is not the largest is 1-16/81 = 65/81

 

Hope this helped