First of all, 2^n and 3^n are exponentials with different bases, and thus their sum cannot be simplified beyond 2^n + 3^n. In other words, these two functions cannot be combined ino one function (such as 4^n).

You may gain much more insight by graphing 2^n, 3^n and 4^n to determine whether there is truth in the given statement or not.

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3 years ago

Scenario 1: You and a friend take turns choosing cards at random from a deck containing 13 red cards and 13 black ones. Once you

Kisachek [45]

Note that both scenarios are similar, the only difference is that in scenario 1, the selected card is not returned to the deck and in scenario 2 the card is returned to the original deck.
Therefore, scenario 1 is dependent, since it "depends" on the selected cards before. If on the first attempt you have 13 blacks and 13 reds and you select a red one, then for the second attempt you will have 13 blacks and 12 reds, so this time you will have more chances of getting a black card. Scenario 2 is independent, because when you return the selected card to the deck you will always have 13 red and 13 black cards in each attempt, so each event will be independent of the previous one. Finally, as it was explained above the probability of selecting two red faces are different in each scenario

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3 years ago