The newest invention is a three-sided die. On any roll of this die, the result is...

The newest invention 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.

A. Find the probability that exactly two of the rolls result in a 3.

B. Given that exactly two of the six rolls resulted in a 1, find the probability that the first roll resulted in a 1.

C. We are told that exactly three of the rolls resulted in a 1 and exactly three rolls resulted in a 2. Given this information, find the probability that the six rolls resulted in the sequence (1,2,1,2,1,2).

Expert Solution

Problem is solved using the Arrangements in case of identical 1's and 2's and3's we find arrangement and probability

Also formula of conditional probability used.

Solution file is attached go through it Thanks

orchestra answered 1 year ago

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