Question

select the correct answer from each drop - down menu. shona spins a spinner with three equal - sized spaces—red, green, and yellow—and then rolls a six - sided die numbered from 1 to 6. the sample size for this compound event is. if instead of three colored spaces, the spinner has four colored spaces, the sample size would be.

Explanation:

Step1: Recall counting - principle for compound events

For two independent events \(A\) and \(B\) with \(n(A)\) and \(n(B)\) possible outcomes respectively, the number of outcomes in the sample - space of the compound event is \(n(A)\times n(B)\).

Step2: Calculate sample size for the first case

The spinner has 3 possible outcomes (\(n_1 = 3\)) and the die has 6 possible outcomes (\(n_2=6\)). Using the counting principle, the sample size \(n=n_1\times n_2 = 3\times6=18\).

Step3: Calculate sample size for the second case

If the spinner has 4 possible outcomes (\(n_3 = 4\)) and the die still has 6 possible outcomes (\(n_2 = 6\)), then the sample size \(n'=n_3\times n_2=4\times6 = 24\).

Answer:

The first blank: 18
The second blank: 24