CountingOutcomes and Theoretical Probability

A computer store sells 4 models of computer (m1,m2,m3 m4. Each model can be fitted with 3 sizes of hard drive (A,B,C,)

1- Find the sample space.

2- What is the probability of choosing a model with a size C hard drive?

3- What is the probability of choosinga model 2 with a size Ahard drive at random?

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1- To find the sample space for this scenario, we need to consider all the possible combinations of computer models and hard drive sizes. The sample space can be represented as the set of all possible outcomes of choosing a computer model and a hard drive size. In this case, we have 4 models (m1, m2, m3, and m4) and 3 sizes of hard drives (A, B, and C). Therefore, the sample space will consist of all 4 models multiplied by all 3 hard drive sizes, resulting in a total of 12 possible outcomes.

2- To find the probability of choosing a model with a size C hard drive, we need to determine the number of outcomes favorable to our event (choosing a model with a size C hard drive), and divide it by the total number of possible outcomes (the sample space).

In this case, the number of outcomes favorable to our event is 4 (since there are 4 computer models, and each model can be fitted with a size C hard drive). The total number of possible outcomes (the sample space) is 12 (as calculated in question 1). Therefore, the probability of choosing a model with a size C hard drive is 4/12 or 1/3.

3- To find the probability of choosing model 2 with a size A hard drive at random, we need to consider all the possible outcomes where we choose model 2 with a size A hard drive, and divide it by the total number of possible outcomes (the sample space).

In this case, there are again 4 outcomes favorable to our event (choosing model 2 with a size A hard drive) since there are 4 models and each model can be fitted with a size A hard drive. The total number of possible outcomes (the sample space) remains 12 (as calculated in question 1). Therefore, the probability of choosing model 2 with a size A hard drive at random is 4/12 or 1/3.