PSAT Math : PSAT Mathematics
Study concepts, example questions & explanations for PSAT Math
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Example Questions
Example Question #231 : Data Analysis
A couple has four children. What is the probability of having exactly three girls?
The total number of possibiliities is 16. The outcome we are looking for is three girls and one boy which happens only four times. Thus the probability becomes 
Example Question #232 : Data Analysis
When a penny is flipped three times in a row, what is the probability of getting all heads or all tails?
The sample space for three coin tosses in a row is 8. Getting all heads can be done only one way. Getting all tails can be done only one way. So the probability of getting all heads or all tails is 
Example Question #233 : Data Analysis
A couple has three children. What is the probability of having exactly two girls or two boys?
The sample space for three children is 8. We can count up what we want or subtract out what we don't want. What we don't want is all boys or all girls.
So the probability becomes
Example Question #234 : Data Analysis
How many different ways can five books be lined up on a shelf?
Order matters, so we use permutations. 
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 #75 : How To Find The Probability Of An Outcome
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 #241 : Data Analysis
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:
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