Question

when a button is pressed, a computer program outputs a random even number greater than 0 and less than 8. you press the button five times. find the number of possible outcomes in the sample space. a) 310 b) 154 c) 243 d) 238

Explanation:

Step1: Identify the range of even numbers

The even numbers greater than 0 and less than 8 are 2, 4, 6.

Step2: Use the multiplication - principle for multiple trials

Since the button is pressed five times and for each press there are 3 possible even - number outcomes, the total number of possible outcomes in the sample space is given by the multiplication principle. If there are \(n_1 = n_2=n_3=n_4=n_5 = 3\) possible outcomes for each of the 5 independent events, the total number of outcomes \(N=n_1\times n_2\times n_3\times n_4\times n_5\).

Step3: Calculate the result

\(N = 3\times3\times3\times3\times3=3^5=243\).

Answer:

C. 243