a Does it matter how many times you have gotten heads before a single coin flip?
B
b What happens to the number of cards and aces in the deck when you draw an ace?
C
c Both hair and eye color depends on the amount of pigment you have.
D
d Do human events dictate the weather?
E
e What is the number of diet sodas in the cooler when your friend took one of them before you?
A
a Independent
B
b Dependent
C
c Dependent
D
d Independent
E
e Dependent
Practice makes perfect
a If you flip a coin one time, you have a 50-50 probability of getting either heads or tails. No matter how many times you flip the coin or what the results were so far, a single coin flip will always have this probability.
Therefore, the number of times you flip the coin or the past outcomes do not affect the probability of the events. The events are independent.
b A deck of cards contain 52 cards, four of which are aces. If you draw two aces, the number of aces is reduced, as are the total number of cards in the deck. This changes the probability of drawing another ace or any other card.
P(first ace)&=4/52 [1em]
P(second ace)&=3/51 [1em]
P(third ace)&=2/50
Therefore, these events are dependent.
c A person's hair and eye color are determined by the same thing: the amount of pigment they have. A blonde person usually has less pigmentation overall, and therefore are more likely to have blue eyes, which is also caused by a low amount of pigmentation.
P(blue eyes & blonde)
>
P(blue eyes & dark hair)
Therefore, these events are dependent.
d Earth's weather is not ruled by events such as the outcome of a debate. It's determined by things such as evaporation and cloud formation. Therefore, these events are independent.
e If your friend has taken a diet soda before you, there is one can of diet soda less in the cooler.
Number of diet sodas
Your friend's case: Your case:
s s-1
This affects the probability of you selecting a diet soda after.
Therefore, these events are dependent.
