AP Statistics : AP Statistics
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Example Questions
Example Question #31 : Probability
If you have a deck of cards, what is the probability that you draw a spade after you drew a non-spade on the first draw without replacement?
You must use the multiplication rule which is the probability of one event happening after one has already taken place is the product of both probabilities. The probability of drawing a non-spade on the first draw is 
Example Question #31 : Probability
Charlene has 7 blue chips, and Karen has 5 green ones. They decide to mix them up in a bag, then Karen will pick 5 chips and Charlene gets the rest.
What is the likelyhood Karen ends up with 5 chips of the same color?
There are 2 ways Karen gets 5 chips of the same color: she gets all 5 greens, or 5 blues. there is only 1 way to get all 5 greens: probability of which can be calculated as;
to calculate p(allblue) we use:
since order doesn't matter and chips are being drawn without replacement, this is an acceptable calculation and summing them yields
Example Question #32 : Probability
A ninja is training for his super secret mission, throwing grappling hooks at targets 
Total likelihood of making the shot = sum of likelihood of making 1st shot+2nd shot+...
1st shot=
2nd shot=.
3rd shot=
4th=
5th=
6th=
Example Question #33 : Probability
Frank of the forest is a monkey man who was raised by chimpanzees from a very young age. He enjoys swinging with his monkey friends. When Frank jumps from one tree to another, the chance that he falls increases by 10% for every foot he jumps past his armspan of 3 feet. (he has a 10% chance of falling at 4ft)
One day, Frank watches his monkey friends do 
Frank knows from experience not to take a jump route if the likelihood of him falling goes above 
Frank can finish this route, none of the jumps have above a 
After 
After 
After 
After 
After
This is multiplication rule. let's calculate the chance frank doesn't fall.
For the first jump this is 
Since the 7th jump drops his survival rate below 
Example Question #1 : How To Identify Independent Events
Given a pair of fair dice, what is the probability of rolling a 7 in one throw?
1/4
5/6
1/2
1/6
1/3
1/6
There are 36 total outcomes for this experiment and there are six ways to roll a 7 with two dice: 1,6; 6,1; 2,5; 5,2; 3,4; and 4,3. Thus, 6/36 = 1/6.
Example Question #1 : How To Identify Independent Events
A fair coin is tossed into the air a total of ten times and the result, heads or tails, is the face landing up. What is the total number of possible outcomes for this experiment?
512
1024
20
2
100
1024
There are two outcomes in each trial of this experiment, and there are ten total trials. Thus, 2 raised to the tenth power yields an answer of 1024.
Example Question #1 : How To Identify Independent Events
Mary randomly selects the king of hearts from a deck of cards. She then replaces the card and again selects one card from the deck. The selection of the second card is a(n)_________ event.
dependent
independent
independent
The selection of the second card is an independent event because it is unaffected by the first event. If the king of hearts had not been replaced, then the probability of selecting a particular card would have been affected by the first event, and the second selection would have been dependent. This, however, is not the case in this question.
Example Question #101 : Ap Statistics
What is the probability of getting a sum of 
The sample space, or total possible outcomes, when rolling two six-sided dice is 
Ways to get what you want:
So there are 
So the probability becomes
Example Question #1 : How To Identify Independent Events
Each answer choice describes two events. Which of the following describes independent events?
A marble is randomly drawn from a bag and set aside. A second marble is drawn from the bag.
One of ten differently colored candies is selected from a jar and eaten. A second candy is then randomly selected.
A card is drawn from a pile and set aside. A second card is drawn.
A coin is flipped in the air and the result is heads. The coin is flipped in the air again.
A shirt is randomly selected from a drawer and is placed in the laundry. A second shirt is randomly slected from the drawer.
A coin is flipped in the air and the result is heads. The coin is flipped in the air again.
Two events are independent of each other when the result of one does not affect the result of the other. In the case of the coin being flipped, the first result in no way influenced the result of the second coin flip. In contrast, when a card is removed from a deck of cards and set aside, that card cannot be selected when a second card is taken from the deck.
Example Question #2 : Independent And Dependent Events
Events 
Because the two events are known to be independent, then the following is true by definition.
This then becomes an algebra problem:
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