Question 832422: Decide if each set of events is independent or dependent. Explain the answer.
1. Cora tosses a number cube. Then she spins a spinner.
2. Kevin chooses a book for a book report from a list of titles. Hiroshi chooses a book for a book report from the remaining titles.
3. Suki picks a coin at random from her wallet. Then she picks a second coin.
Answer by neatmath(302)   (Show Source):
You can put this solution on YOUR website!
1. If you toss a number cube, will it have any effect on what comes up on the spinner? No, right? Then those events are independent.
A good example of this would be if I flip a coin right this minute, and you pull a random sock out of your drawer, would it matter if I got heads on the coin? Would it affect the probability that you pulled a green sock out of your drawer. It would not. Those are also independent events!
2. Conversely, given a group of books, does Kevin's choice of book impact Hiroshi's choice of books? Definitely, as Hiroshi can only choose from the leftover books. These events are dependent, as it is implied that Hiroshi can not choose the same book title that Kevin chose.
If Hiroshi COULD choose the same book title that Kevin chose, then those events would be independent.
3. Lastly, Suki has a limited number of coins in her wallet. If she chooses one at random, the next one she chooses will be dependent on what her first choice happened to be.
As an example, let's say she has 10 coins: 1 quarter and 9 pennies.
If her first random choice of a coin is a quarter, could she ever pull another quarter out of the remaining 9 coins? No, thus these events are also dependent, much like the book situation in Problem 2.
I hope this helps! Keep practicing! :)
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