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PSAT Math : Statistics

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Example Questions

Example Question #1521 : Psat Mathematics

When a penny is flipped three times in a row, what is the probability of getting all heads or all tails?

Possible Answers:

$\frac{1}{3}$

$\frac{3}{8}$

$\frac{1}{6}$

$\frac{1}{4}$

$\frac{1}{8}$

Correct answer:

$\frac{1}{4}$

Explanation:

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 $\frac{2}{8}$ or $\frac{1}{4}$ .

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Example Question #72 : Probability

A couple has three children. What is the probability of having exactly two girls or two boys?

Possible Answers:

$\frac{3}{4}$

$\frac{1}{8}$

$\frac{2}{3}$

$\frac{3}{8}$

$\frac{1}{2}$

Correct answer:

$\frac{3}{4}$

Explanation:

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 $1 - \frac{2}{8} = \frac{6}{8} = \frac{3}{4}$

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Example Question #1522 : Psat Mathematics

How many different ways can five books be lined up on a shelf?

Possible Answers:

150

120

130

Correct answer:

120

Explanation:

Order matters, so we use permutations. $_{5}^{5}\textrm{P}$ is $5\cdot 4\cdot 3\cdot 2\cdot 1 = 120$

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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?

Possible Answers:

150

108

125

Correct answer:

108

Explanation:

Choosing one of each clothing item is an independent event and should be multiplied together. So the answer becomes

$shirts\times pants\times socks\times shoes$

$6 \cdot 3 \cdot 2 \cdot 3 = 108$ different combinations.

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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?

Possible Answers:

$\frac{1}{8}$

$\frac{7}{1680}$

$\frac{3}{1024}$

$\frac{12}{140}$

$\frac{1}{140}$

Correct answer:

$\frac{1}{140}$

Explanation:

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:

$P=\frac{3}{8}\cdot \frac{2}{7}\cdot \frac{2}{6}\cdot \frac{1}{5}=\frac{12}{1680}=\frac{1}{140}$

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Example Question #1523 : Psat Mathematics

If you flip a fair coin four times in a row, what is the probability of getting at least one head?

Possible Answers:

$\frac{5}{8}$

$\frac{3}{8}$

$\frac{1}{16}$

$\frac{15}{16}$

$\frac{1}{4}$

Correct answer:

$\frac{15}{16}$

Explanation:

$1-P(no\ heads)=P(at\ least\ one\ heads)$

There are 16 different ways to flip a fair coin four times in a row. There is only one way to get all tails.

$P(no\ heads)=\frac{1}{16}$

so the $P(at\ least\ one\ heads)=1-\frac{1}{16}=\frac{15}{16}$

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Example Question #72 : How To Find The Probability Of An Outcome

When rolling two standard six-sided dice, what is the probability of getting five or less?

Possible Answers:

$\frac{3}{8}$

$\frac{7}{12}$

$\frac{5}{16}$

$\frac{5}{18}$

$\frac{1}{6}$

Correct answer:

$\frac{5}{18}$

Explanation:

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 $\frac{10}{36}=\frac{5}{18}$ .

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Example Question #1524 : Psat Mathematics

How many different ways can five books be lined up on a shelf?

Possible Answers:

$120$

$75$

$25$

$225$

$90$

Correct answer:

$120$

Explanation:

Order matters, so we use permutations: $_{5}^{5}\textrm{P}$ = $5\times 4\times 3\times 2\times 1=120$ .

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Example Question #81 : Probability

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?

Possible Answers:

None of the other answers

$\frac{1}{2}$

$\frac{45}{88}$

$\frac{43}{88}$

$\frac{43}{90}$

Correct answer:

$\frac{45}{88}$

Explanation:

Half of the scrunchies are black, so

$90\times \frac{1}{2}=45\hspace{1 mm}black\hspace{1 mm}scrunchies$

One third of the scrunchies are white

$90\times \frac{1}{3}=30\hspace{1 mm}white\hspace{1 mm}scrunchies$

One ninth of the scrunchies are blue

$90\times \frac{1}{9}=10\hspace{1 mm}blue\hspace{1 mm}scrunchies$

And the rest are green:

$90-45-30-10=5\hspace{1 mm}green\hspace{1 mm}scrunchies$

If we have already drawn two, our total amount of scrunchies is now 88, so the probability of pulling a black scrunchie will be:

$\frac{45}{88}$

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Example Question #201 : Data Analysis

There is a classroom of 60 students. $\frac{7}{12}$ of the students are wearing red shirts, $\frac{1}{3}$ of the students are wearing pink shirts, and the rest of the students are wearing orange shirts. What is the probability of randomly selecting the name of a student wearing an orange shirt?

Possible Answers:

$\frac{2}{25}$

$\frac{1}{6}$

$\frac{1}{12}$

$8.3\%$

None of the available answers

Correct answer:

$\frac{1}{12}$

Explanation:

$\frac{7}{12}$ of the students are wearing red shirts, and

$\frac{7}{12}\times 60=\frac{7}{1}\times 5=35\hspace{1 mm}students$

One third of the students are wearing pink shirts

$\frac{1}{3}\times 60=\frac{1}{1}\times 20=20\hspace{1 mm}students$

The remaining students are wearing orange

$60-35-20=5\hspace{1 mm}students$

The probability of randomly selecting a student wearing an orange shirt is

$\frac{5}{60}=\frac{1}{12}$

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PSAT Math : Statistics

Study concepts, example questions & explanations for PSAT Math

All PSAT Math Resources

Example Questions

Example Question #1521 : Psat Mathematics

Example Question #72 : Probability

Example Question #1522 : Psat Mathematics

Example Question #72 : How To Find The Probability Of An Outcome

Example Question #76 : Outcomes

Example Question #1523 : Psat Mathematics

Example Question #72 : How To Find The Probability Of An Outcome

Example Question #1524 : Psat Mathematics

Example Question #81 : Probability

Example Question #201 : Data Analysis

All PSAT Math Resources

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