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Common Core: 7th Grade Math : Grade 7

Study concepts, example questions & explanations for Common Core: 7th Grade Math

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All Common Core: 7th Grade Math Resources

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Example Questions

Example Question #781 : Grade 7

There are 6 red marbles, 4 purple marbles, and 9 green marbles in a bag. What is the probablility of randomly drawing a green marble?

Possible Answers:

$\frac{9}{19}$

$\frac{2}{3}$

$\frac{3}{4}$

$\frac{3}{7}$

Correct answer:

$\frac{9}{19}$

Explanation:

First we need to determine the total number of marbles in the bag:

$\dpi{100} 6+4+9=19\ marbles$

There are 9 green marbles, so the probability of drawing one of those 9 marbles out of 19 possible marbles is $\dpi{100} \frac{9}{19}$ .

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Example Question #782 : Grade 7

A bag contains $\small 2$ red marbles, $\small 7$ pink marbles, and $\small 6$ purple marbles. What is the probability of not choosing a purple marble?

Possible Answers:

$\small \frac{2}{3}$

$\small \frac{2}{5}$

$\small \frac{3}{5}$

$\small \frac{3}2$

Correct answer:

$\small \frac{3}{5}$

Explanation:

The probability (p) is equal to the number of a specific event (purple marbles) divided by the total number of events. The probability of NOT p (called q) is equal to $\small 1-q.$ In this example:

$\small P_{purple}=\frac{6}{2+7+6}=\frac{6}{15}=\frac{2}{5}$

$\small Q_{not\ purple}=1-\frac{2}{5}=\frac{3}{5}$

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Example Question #783 : Grade 7

A bag of marbles contains 8 black marbles, 4 red marbles, 3 blue marbles, and 5 white marbles. What is the probability of not drawing a black marble?

Possible Answers:

$\frac{1}{8}$

$\frac{4}{5}$

$\frac{3}{5}$

$\frac{7}{8}$

$\frac{2}{5}$

Correct answer:

$\frac{3}{5}$

Explanation:

Probability is determined by dividing the possible number of instances of a particular outcome by the total number of possible outcomes. Therefore, we need to find the probability of drawing red, blue, or white divided by the total number of outcomes.

$\small P=\frac{instances\ of\ red,\ white,\ and\ blue}{total\ instances}$

$P==\frac{4+3+5}{4+3+5+8}=\frac{12}{20}=\frac{3}{5}$

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Example Question #784 : Grade 7

If you meet a random person on the street, what is the probability he or she was born on a weekend?

Possible Answers:

$P=\frac{2}{7}$

$P=\frac{1}{7}$

$P=\frac{3}{7}$

$P=\frac{1}{12}$

$P=\frac{2}{52}$

Correct answer:

$P=\frac{2}{7}$

Explanation:

There are seven days in a week.

The probability that a person you meet was born on any particular day is $\tiny \frac{1}{7}$ .

The question asks for the probability that the person you meet was born on a weekend (Saturday or Sunday). Therefore, we must add the probability of being born on either day:

$P=\frac{1}{7}+\frac{1}{7}=\frac{2}{7}$

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Example Question #781 : Grade 7

There are 4 green marbles, 5 yellow marbles, and 3 red marbles in a bag. If one is picked out of the bag at random, what is the probability that it will be a red marble?

Possible Answers:

$\frac{1}{3}$

$\frac{5}{12}$

$\frac{3}{4}$

$\frac{11}{12}$

$\frac{1}{4}$

Correct answer:

$\frac{1}{4}$

Explanation:

To find probability, you have to consider part over whole. The total number of marbles is 12. Then, identify how many red marbles there are (3). From there, you can make a fraction $\left(\frac{3}{12}\right)$ , which can be simplified to $\frac{1}{4}$ .

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Example Question #73 : Statistics & Probability

A pair of fair dice are thrown. Which of these events has probability $\frac{1}{9}$ ?

Possible Answers:

The sum of the dice is 5

Both dice show the same number

The sum of the dice is 10

The sum of the dice is divisible by 6

The sum of the dice is 4.

Correct answer:

The sum of the dice is 5

Explanation:

One-ninth of the 36 possible rolls is 4, so we are looking for an outcome that can happen four ways.

There are 6 ways that both dice can show the same number - double 1, double 2, and so forth.

There are 3 ways to roll a sum of 10: (4,6), (5,5), and (6,4).

There are 6 ways to roll a sum divisible by 6: (1,5), (2,4), (3,3), (4,2), and (5,1) all yield 6, and (6,6) yields 12.

There are 4 ways to roll a sum of 5: (1,4), (2,3), (3,2), and (4,1).

There are 3 ways to roll a sum of 4: (1,3), (2,2), (3,1).

The correct choice is the event that the sum of the dice is 5.

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Example Question #74 : Statistics & Probability

Gina has a bag of 12 marbles. The bag is half black marbles and half white marbles. If Gina picks out two random marbles, and both are white, what is the percent chance that the next marble she picks will also be white?

Possible Answers:

60 percent

20 percent

50 percent

40 percent

Correct answer:

40 percent

Explanation:

Given that in Gina’s bag of 12 marbles, half of them are black and half are white, this means that there are 6 black marbles and 6 white marbles. However, because she already picked out 2 white marbles, this means that there are now only 4 out of 10 white marbles left. 4 out of 10 converts to 40 percent, which is therefore the correct answer.

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Example Question #785 : Grade 7

10% of puppies are born with spots. Of those, 50% have black spots. What is the percentage of puppies who have black spots?

Possible Answers:

$20\%$

$12\%$

$10\%$

$5\%$

$15\%$

Correct answer:

$5\%$

Explanation:

If 10 percent of puppies are born with spots, and of those, 50 percent have black spots, then the total percent of puppies who have spots AND the color of the spots is black can be found by multiplying the two percentages by one another:

$10\%\times50\%=0.10\times0.50=0.05$

0.05 is the equivalent of 5 percent, the correct answer.

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Example Question #14 : How To Find The Probability Of An Outcome

Jenny entered a raffle with 9 other participants. The raffle ticket numbers are:

288, 289, 290, 291, 292, 292, 294, 295, 296, 297

Jenny's ticket is 288. The raffler begins to announce the winning ticket. The first digits are 2 and 8. He is about to announce the third digit.

What are the chances that Jenny won?

Possible Answers:

$100\%$

$20\%$

$0\%$

$33.33\%$

$50\%$

Correct answer:

$50\%$

Explanation:

There are 10 total participants in the raffle.

288, 289, 290, 291, 292, 292, 294, 295, 296, 297

Only 2 participants have tickets with numbers that beging in 2 and 8.; therefore, Jenny has a 50 percent chance of holding the winning raffle ticket.

The winner is either 288 or 289, leaving Jenny a 50 percent chance.

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Example Question #786 : Grade 7

At a party, there are 5 girls and 5 boys. There is a raffle, and each girl gets twice as many raffle tickets as each boy. Tracy is one of the girls at the party. What is the chance of her winning the raffle if each boy gets 7 raffle tickets?

Possible Answers:

$\frac{2}{15}$

$\frac{1}{7}$

$\frac{2}{7}$

$\frac{1}{15}$

Correct answer:

$\frac{2}{15}$

Explanation:

If each boy gets 7 raffle tickets, that means that each girl gets 14 raffle tickets.

Therefore, Tracy will have 14 raffle tickets, and the total number of raffle tickets will be equal to $5\cdot7+5\cdot14$ .

Thus, Tracy's chance of winning will be equal to:

$\frac{14}{5\cdot 7+5\cdot 14}$

$\frac{14}{7(5+5\cdot 2)}$

$\frac{2}{(5+10)}$

$\frac{2}{15}$

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Common Core: 7th Grade Math : Grade 7

Study concepts, example questions & explanations for Common Core: 7th Grade Math

All Common Core: 7th Grade Math Resources

Example Questions

Example Question #781 : Grade 7

Example Question #782 : Grade 7

Example Question #783 : Grade 7

Example Question #784 : Grade 7

Example Question #781 : Grade 7

Example Question #73 : Statistics & Probability

Example Question #74 : Statistics & Probability

Example Question #785 : Grade 7

Example Question #14 : How To Find The Probability Of An Outcome

Example Question #786 : Grade 7

All Common Core: 7th Grade Math Resources

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