Question

at a game show, there are three doors marked 1, 2, and 3. a contestant is allowed to select one of three keys labeled a, b, and c and then use it to open one of the doors. the sample space showing the ways in which a contestant can select a key and a door is represented in the table.

what is the missing term in the table? if there were two doors instead of three doors, what would the sample size be?

a. the missing term is a - 2. the sample size would be 6
b. the missing term is c - 2. the sample size would be 8
c. the missing term is c - 2. the sample size would be 9
d. the missing term is b - 2. the sample size would be 12

Explanation:

Step1: Find the missing term

By observing the table, we can see that for each door number, there are three keys (A, B, C). For door 2, the key - door combinations follow the pattern. The missing term is A - 2.

Step2: Calculate the sample size when there are 2 doors

The formula for the number of elements in a sample space (when choosing one key and one door) is \(n = \text{Number of keys}\times\text{Number of doors}\). Initially, with 3 keys and 3 doors, the sample size \(n_1=3\times3 = 9\). If the number of doors \(d = 2\) and the number of keys \(k=3\), then the sample size \(n=k\times d\). Substituting \(k = 3\) and \(d=2\), we get \(n=3\times2=6\)

Answer:

A. The missing term is A - 2. The sample size would be 6.