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ISEE Middle Level Math : Probability

Study concepts, example questions & explanations for ISEE Middle Level Math

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All ISEE Middle Level Math Resources

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Example Questions

Example Question #1 : Probability

There are 32 marbles in a bag: 7 are Red, 11 are Blue, 8 are Purple and 6 are Green. If I pick one marble out of the bag, which color would it most likely be?

Possible Answers:

Purple

Red

Green

Blue

Correct answer:

Blue

Explanation:

Find the color with the largest number of marbles in the bag.

Answer: There are more blue marbles in the bag, therefore it would be more likely to pick a blue marble.

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Example Question #771 : Grade 7

The red queens are removed from a standard deck of fifty-two cards. What is the probability that a card randomly drawn from that modified deck will be a face card (jack, queen, king)?

Possible Answers:

$\frac{6}{25}$

$\frac{1}{5}$

$\frac{1}{3}$

$\frac{1}{4}$

$\frac{5}{26}$

Correct answer:

$\frac{1}{5}$

Explanation:

There are four cards of each rank in a standard deck; since three ranks - jacks, queens, kings - are considered face cards, this makes twelve face cards out of the fifty-two. But two of those face cards - two red queens - have been removed, so now there are ten face cards out of fifty. This makes the probability of a randomly drawn card being a face card

$\frac{10}{50} = \frac{1}{5}$ .

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Example Question #772 : Grade 7

Jamie rolled a normal 6-sided die. What is the probability of rolling a number greater than 4?

Possible Answers:

1/4

1/2

1/3

1/6

Correct answer:

1/3

Explanation:

Probability is determined by dividing the number of incidences of a specific outcome (in this case rolling greater than 4, or rolling a 5 or 6) by the total number of outcomes (there are 6 sides to the die).

$P=\frac{2}{6}=\frac{1}{3}$

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Example Question #2 : Outcomes

What is the probability of drawing a diamond from a regular set of playing cards?

Possible Answers:

$\frac{1}{8}$

$\frac{1}{13}$

$\frac{1}{4}$

$\frac{1}{26}$

Correct answer:

$\frac{1}{4}$

Explanation:

Probability is determined by dividing the number of outcomes of a particular event by the total number of events. In a regular deck of playing cards, there are 52 cards and 13 diamonds.

$P=\frac{13}{52}=\frac{1}{4}$

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Example Question #3 : Outcomes

What is the probability of drawing a red jack from a standard deck of playing cards?

Possible Answers:

$P=\frac{1}{13}$

$P=\frac{1}{26}$

$P=\frac{2}{13}$

$P=\frac{1}{52}$

Correct answer:

$P=\frac{1}{26}$

Explanation:

A standard deck contains cards including jacks, of which are red. Therefore, the probability is:

$P=\frac{2}{52}=\frac{1}{26}$

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Example Question #773 : Grade 7

There are 5 yellow pebbles, 12 orange pebbles, and 8 red pebbles. What is the probability of picking a red or yellow pebble?

Possible Answers:

$\frac{5}{25}$

$\frac{12}{25}$

$\frac{13}{24}$

$\frac{8}{25}$

$\frac{13}{25}$

Correct answer:

$\frac{13}{25}$

Explanation:

There are 13 yellow and red pebbles. There are 25 pebbles total. Therefor the probability of choosing a red or yellow pebble is $\frac{13}{25}$ .

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Example Question #2 : Probability

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:

$\frac{3}{4}$

$\frac{9}{19}$

$\frac{3}{7}$

$\frac{2}{3}$

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 #5 : Outcomes

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:

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

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

$\small \frac{3}2$

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

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 #2 : Probability

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:

$\frac{7}{8}$

$\frac{2}{5}$

$\frac{4}{5}$

$\frac{1}{8}$

$\frac{3}{5}$

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 #3 : Probability

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

Possible Answers:

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

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

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

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

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

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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All ISEE Middle Level Math Resources

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ISEE Middle Level Math : Probability

Study concepts, example questions & explanations for ISEE Middle Level Math

All ISEE Middle Level Math Resources

Example Questions

Example Question #1 : Probability

Example Question #771 : Grade 7

Example Question #772 : Grade 7

Example Question #2 : Outcomes

Example Question #3 : Outcomes

Example Question #773 : Grade 7

Example Question #2 : Probability

Example Question #5 : Outcomes

Example Question #2 : Probability

Example Question #3 : Probability

All ISEE Middle Level Math Resources

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