Question

1. you choose a movie cd at random from a case containing 8 comedy cds, 5 science fiction cds, and 7 adventure cds. the cd is not a comedy.
2. you roll a number cube. you roll a number that is greater than 2 and less than 5.
3. communicate mathematical ideas the theoretical probability of a given event is \\(\frac{9}{13}\\). explain what each number represents.

Explanation:

Question 13

Step1: Find total number of CDs

Total CDs = Comedy + Science Fiction + Adventure = \( 8 + 5 + 7 = 20 \)

Step2: Find number of non - comedy CDs

Non - comedy CDs = Science Fiction + Adventure = \( 5 + 7 = 12 \)

Step3: Calculate probability

Probability (not comedy) = \( \frac{\text{Number of non - comedy CDs}}{\text{Total number of CDs}}=\frac{12}{20}=\frac{3}{5} \)

Step1: Determine possible outcomes on a number cube

A number cube has numbers from 1 to 6. The numbers greater than 2 and less than 5 are 3 and 4. So, there are 2 favorable outcomes.

Step2: Determine total number of outcomes

Total number of outcomes when rolling a number cube is 6.

Step3: Calculate probability

Probability = \( \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}=\frac{2}{6}=\frac{1}{3} \)

In the theoretical probability formula \( P(E)=\frac{\text{Number of favorable outcomes}}{\text{Number of possible outcomes}} \), for the probability \( \frac{9}{13} \), the number 9 represents the number of favorable outcomes (the number of outcomes in the sample space that correspond to the event), and the number 13 represents the total number of possible outcomes in the sample space (the total number of equally - likely outcomes).

Answer:

\(\frac{3}{5}\)

Question 14