Question

A card is drawn from a five-card hand. The cards are labeled A, B, C, D, F. Then a spinner with 3 sections labeled as 1, 2, 3 is spun. What is the sample space?

Answer 1

Answer:

The sample space is the set of all the possible outcomes of a given experiment.

Here, our experiment consists on:

Drawing a card from a five-card hand, such that the outcomes there are:

A, B, C, D, E  (5 outcomes)

Followed by spinning a spinner with 3 sections labeled 1, 2 and 3 (3 outcomes).

The total number of outcomes of the combined event, is equal to the product between the numbers of outcomes for each event.

So for our experiment, the total number of outcomes is:

C = 5*3 = 15 outcomes.

And these outcomes are like:

Drawing the card A and spinning a 1 (represented with A-1)

Drawing the card C and spinning a 2 (represented with C-2)

etc.

The set of all possible outcomes are:

{A-1, A-2, A-3, B-1, B-2, B-3, C-1, C-2, C-3, D-1, D-2, D-3, F-1, F-2, F-3}