Question

which of the following events are independent? refer to the math notes in this lesson.
a. flipping a head, after flipping 5 heads in a row.
hint (a):
does one flip affect the next one?
b. drawing an ace from a deck of playing cards, after two aces were just drawn (and not returned to the deck).
hint (b):
since the aces are not returned to the deck, the total number of cards is different for the next draw.
c. having blue eyes, if you have blonde hair.
d. the probability of rain this weekend, if the debate team from north city high school wins the state championship.
e. randomly selecting a diet soda from a cooler filled with both diet and regular soda, after the person before you just selected a diet soda and drank it.
hint (e):
has the probability changed after the first selection?

Explanation:

• For event a: Flipping a coin is an independent event. The outcome of one flip does not affect the outcome of another flip. So, flipping a head after flipping 5 heads in a row is independent.
• For event b: Since the aces are not returned to the deck, the probability of drawing an ace in the next draw is affected by the previous draws. So, it is a dependent event.
• For event c: Having blonde hair and having blue eyes are two different characteristics. The probability of having blue eyes is not affected by having blonde hair. So, it is an independent event.
• For event d: The probability of rain this weekend is not affected by the debate team from North City High School winning the state championship. So, it is an independent event.
• For event e: After one diet soda is selected and drunk, the number of diet sodas and the total number of sodas in the cooler change. So, the probability of randomly selecting a diet soda is affected. It is a dependent event.

Answer:

A. Flipping a head, after flipping 5 heads in a row.
C. Having blue eyes, if you have blonde hair.
D. The probability of rain this weekend, if the debate team from North City High School wins the state championship.