Question

ruth has a box containing music cds. each cd contains songs from only one of these three genres: pop (p), hip - hop (h), and rock (r). she picks one cd from the box, replaces it, and then picks another cd. the sample space for this event is listed.
sample space
p - p h - p r - p
p - h h - h r - h
p - r r - r
what is the missing term for this compound event? what is the sample size?
a. the missing term is h - p and the sample size is 9
b. the missing term is h - r and the sample size is 9
c. the missing term is h - p and the sample size is 3
d. the missing term is h - r and the sample size is 3

Explanation:

Step1: List all possible combinations

There are 3 genres (P, H, R). When picking two CDs with replacement, we consider all pairs. The first - letter of each pair represents the first pick and the second - letter represents the second pick. The possible pairs are formed by multiplying the number of choices for the first pick (3) by the number of choices for the second pick (3).

Step2: Identify the missing pair

The pairs listed are PP, HP, RP, PH, HH, RH, PR, RR. The missing pair from the set of all possible pairs of the three - genre combinations is HR.

Step3: Calculate the sample size

Since there are 3 choices for the first pick and 3 choices for the second pick, using the multiplication principle of counting, the sample size \(n = 3\times3=9\).

Answer:

B. The missing term is H - R and the sample size is 9