SAT Math : SAT Mathematics
Study concepts, example questions & explanations for SAT Math
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Example Questions
Example Question #72 : How To Find The Probability Of An Outcome
Jimmy is having trouble choosing what to wear to the baseball game. He has six shirts, three pants, two pairs of socks and three pairs of shoes. How many different outfits does Jimmy have to choose from?
Choosing one of each clothing item is an independent event and should be multiplied together. So the answer becomes
or
Example Question #76 : Outcomes
Joe has eight marbles: 3 Red, 2 Green, 2 Blue and 1 Yellow.
If Joe puts the marbles into a bag and draws out four, what are the odds that he gets exactly one of each color?
The probabilities of each pick changes as fewer marbles remain in the bag. Each selection order of the colors will yield the same probability, expressed as:
Example Question #76 : Outcomes
If you flip a fair coin four times in a row, what is the probability of getting at least one head?
There are 16 different ways to flip a fair coin four times in a row. There is only one way to get all tails.
so the
Example Question #74 : Probability
When rolling two standard six-sided dice, what is the probability of getting five or less?
The sample space for rolling two six-sided dice is 36.
Counting the wanted outcomes gives:
2: 1,1 (1)
3: 1,2 and 2,1 (2)
4: 1,3 and 2,2 and 3,1 (3)
5: 1,4 and 2,3 and 3,2 and 4,1 (4)
So there are 10 ways to get a five or less.
Thus the probability of getting a five or less is 
Example Question #3161 : Sat Mathematics
How many different ways can five books be lined up on a shelf?
Order matters, so we use permutations: 
Example Question #3162 : Sat Mathematics
You have a box of 90 colored scrunchies. Half of the scrunchies are black, one third of the scrunchies are white, one ninth of the scrunchies are blue, and the rest are green. You pull the scrunchies from the box at random.
The first scrunchie you pick up is blue. The second scrunchie is green. What is the probability that the third scrunchie you pick up will be black?
None of the other answers
Half of the scrunchies are black, so
One third of the scrunchies are white
One ninth of the scrunchies are blue
And the rest are green:
If we have already drawn two, our total amount of scrunchies is now 88, so the probability of pulling a black scrunchie will be:
Example Question #3162 : Sat Mathematics
There is a classroom of 60 students. 
None of the available answers
One third of the students are wearing pink shirts
The remaining students are wearing orange
The probability of randomly selecting a student wearing an orange shirt is
Example Question #3163 : Sat Mathematics
A bag of colored candies has ten red candies, 14 purple candies, 12 orange candies, and 4 yellow candies. What is the ratio of yellow to orange candies in the bag?
There are four yellow candies, and 12 orange candies, so the raio is:
The ratio of yellow to orange candies is 1:3
Example Question #83 : Probability
Recall:
Consequently, the probability that the person selected is Asian is:
Similarly, the probability that a randomly selected Asian person is also female is:
Finally, the probability of 2 unrelated events occuring is equal to the product of the individual probabilities of the 2 events. Therefore the probability of selecting an Asian female is
Example Question #3164 : Sat Mathematics
Fred wants to put together outfits that he can wear for the day. He can wear any type of outfit for school, but he needs to wear formal attire for dinner later. He can either choose to wear something all day or choose to change clothes before going out to dinner.
If Fred has 2 formal shirts and 3 informal shirts, 1 pair of formal pants and 2 pairs of informal pants, and 1 pair of formal shoes and 1 pair of informal shoes, how many different ways could Fred appear for school and then dinner, allowing for changing in between?
Fred can wear anything to school. This means he can wear either formal things or informal things. He has 3 informal shirts and 2 formal shirts. This means he has a total of 5 shirts to choose from when deciding what to wear. Similarly, he has 3 pairs of pants and 2 pairs of shoes to choose from. After choosing a shirt (5 options), he chooses pants (3 options) and shoes (2 options) resulting in 
Fred must wear formal attire to the dinner. This means that Fred can only choose between his 2 formal shirts, his formal pair of pants, and his formal shoes. Since he only has a choice of shirts, he ends up only having 2 choices to make in outfits.
To figure out how many ways he can dress throughout the day, we simply choose an outfit for school and an outfit for dinner. We have 30 choices for what to wear to school and 2 choices to wear to dinner, giving us
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