Question

sasha chooses one of these cards from a deck. then, she puts the card back in the deck and chooses a card again. 1 3 5 7 9 which table represents the sample space of this compound event?

Explanation:

Step1: Identify the compound - event

Sasha is choosing a card twice with replacement from the set {1, 3, 5, 7, 9}.

Step2: Determine the sample - space concept

The sample space of a compound event of two independent trials is the set of all ordered pairs of the possible outcomes of each trial.

Step3: Analyze each table

For the first draw, there are 5 possible outcomes (1, 3, 5, 7, 9), and for each of these 5 outcomes, on the second draw, there are again 5 possible outcomes. The sample - space should have all pairs (a, b) where a and b are from the set {1, 3, 5, 7, 9}.
The first table (top - left) represents the correct sample space as it has all possible ordered pairs of the numbers 1, 3, 5, 7, 9. For example, when the first card is 1, the second card can be 1, 3, 5, 7, or 9 giving the pairs (1,1), (1,3), (1,5), (1,7), (1,9) and so on for all first - draw values.

Answer:

The top - left table represents the sample space of this compound event.