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 if the person before you took one of them?
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, the next coin flip will always have this probability. Therefore, the results of the previous coin flips do not affect the probability of the result of the next coin flip. The events are independent.
b A deck of cards contain 52 cards, 4 of which are aces. If you draw 2 aces, the number of aces is reduced, as is 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 is more likely to have blue eyes, which is also caused by a low amount of pigmentation. Therefore, these events are dependent.
d Earth's weather is not determined by events such as the outcome of a debate. It is determined by things such as evaporation and cloud formation. Therefore, these events are independent.
e If the person before you has just taken a diet soda, there is one fewer cans of diet soda, and one fewer cans of soda overall, in the cooler. This affects the probability of you randomly selecting a diet soda. Therefore, these events are dependent.
