Question

you flip a coin, pick a card, and spin the spinner. how many outcomes are possible?

Explanation:

Step1: Determine coin - flip outcomes

There are 2 possible outcomes (heads or tails) when flipping a coin, so $n_1 = 2$.

Step2: Determine card - pick outcomes

There are 3 possible outcomes when picking a card (I, J, K), so $n_2=3$.

Step3: Determine spinner - spin outcomes

There are 5 possible outcomes when spinning the spinner (1, 2, 3, 4, 5), so $n_3 = 5$.

Step4: Use the multiplication principle

The total number of possible outcomes is the product of the number of outcomes of each event. So the total number of outcomes $N=n_1\times n_2\times n_3$.
$N = 2\times3\times5$
$N=30$

Answer:

30