joseph chooses one of these cards from a deck. then he puts the card back in the deck and chooses a card…

joseph chooses one of these cards from a deck. then he puts the card back in the deck and chooses a card again. 7 8 9 which tree - diagram represents the sample space of this compound event?

joseph chooses one of these cards from a deck. then he puts the card back in the deck and chooses a card again. 7 8 9 which tree - diagram represents the sample space of this compound event?

Answer

Explanation:

Step1: Analyze first - draw possibilities

The first - draw can result in either 7, 8, or 9.

Step2: Analyze second - draw possibilities

Since the card is replaced, for each outcome of the first - draw (7, 8, or 9), the second - draw can also result in 7, 8, or 9. The correct tree - diagram should have three branches starting from the root for the first - draw (labeled 7, 8, 9), and from each of these three branches, there should be three more branches (also labeled 7, 8, 9) for the second - draw.

Answer:

The first tree - diagram (where the first level of branches is labeled 7, 7, 7 and from each of these 7 - branches, there are branches labeled 8 and 9) represents the sample space correctly as it shows all possible combinations of the two draws with replacement.