The intelligence of a character in a game similar to Dungeons & Dragons is deter

Question

The intelligence of a character in a game similar to Dungeons & Dragons is determined by rolling the four-sided die twice and adding 1 to the sum of the numbers. A four-sided die has faces with one of the numbers 1, 2, 3, or 4, appearing at the bottom of each visible face. Assume that the die is perfectly balanced. Give a probability model (sample space and probabilities of outcomes) for the character's intelligence. Follow the method used in these examples. What is the sample space of the character's intelligence? S={2, 3, 4, 5, 6, 7,8) Os={3, 5,7,9) S- (4, 6, 8 Os={1, 2, 3, 4, 5, 6, 7, 8, 9} O S-(3, 4, 5,6, 7, 8, 9) In this probability model, what is the probability of intelligence = 47( Enter an exact number as an integer, fraction, or decimal.) In this probability model, what is the probability of intelligence9? (Enter an exact number as an integer, fraction, or decimal.) In this probability model, what is the probability of intelligence 11? (Enter an exact number as an integer, fraction, or decimal.) eBook

Explanation / Answer

as we add sum of roll of two dice and 1.

sample space is {3,4,5,6,7,8,9}

probability of intelligence =4 =P(X=4)= P(first roll 1 and second 2+first roll 2 and second 1) =(1/4)*(1/4)+(1/4)*(1/4)

=1/8

probability of intelligence =9=P(X=9)=P(both rolls are 4) =(1/4)*(1/4) =1/16

probability of intelligence =11=P(X=11)=0 (As no outcome is 11)

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