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Alicia rolls two fair number cubes numbered from 1 to 6. She first defines the sample space, as shown below:


(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6)

(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6)

(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6)

(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6)

(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6)

(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)


Based on the sample space, what is the probability of getting a total of 7?

Verified Answer :

dalendrk

\(\Omega=\{(x;\ y):x\wedge y\in\{1;\ 2;\ 3;\ ...;\ 6\}\}\\\\|\Omega|=6^2=36\\\\A=\{(1;\ 6);\ (2;\ 5);\ (3;\ 4);\ (4;\ 3);\ (5;\ 2);\ (6;\ 1)\}\\\\|A|=6\\\\P(A)=\dfrac{|A|}{|\Omega|}\to\boxed{P(A)=\dfrac{6}{36}=\dfrac{1}{6}}\)

The probability is the ratio of the favorable event to the total number of events. Then the probability of getting a total of 7 will be 16.67%.

What is probability?

Probability means possibility. It deals with the occurrence of a random event. The value of probability can only be from 0 to 1. Its basic meaning is something is likely to happen.

Alicia rolls two fair number cubes numbered from 1 to 6.

The total event will be

Total event = 36

She first defines the sample space, as shown below:

(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6)

(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6)

(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6)

(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6)

(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6)

(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)

Then the probability of getting a total of 7 will be

Favorable event = 6 {(6, 1)(5, 2)(4, 3)(3, 4)(2, 5)(1, 6)}

Then we have

\(P = \dfrac{6}{36} = 0.1667 \ or \ 16.67\%\)

More about the probability link is given below.

https://brainly.com/question/795909

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