Probability - ISEE Lower Level (grades 5-6) Mathematics Achievement

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Question

Jen has a bag of 16 marbles. In the bag, there are 8 green marbles, 4 white, and 4 red marbles. If Jen reaches in and randomly chooses a marble, what is the probability (expressed as a percentage) that she chooses a white marble?

Answer

The chance of choosing a white marble is out of , or $\dpi{100} \frac{1}{4}$

$\dpi{100} \frac{1}{4}$ expressed as a percentage is

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Question

If Jennifer has a bag of hair ties that contains $\small 1$ blue hair tie, $\small 2$ green hair ties, $\small 3$ pink hair ties, and $\small 1$ purple hair tie, and she grabs one at random, what is the probability she will grab a green hair tie?

Answer

First we must determine how many hair ties are in the bag by adding all of them together.

$\small 1+2+3+1=7$

We know from the information provided in the problem that there are $\small 2$ green hair ties in the bag, so the probability of Jennifer grabbing one green hair tie from the seven possible hair ties is $\small \small \frac{2}{7}$ .

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Question

If Brian has a box of toy cars that contains $\small 3$ blue cars, $\small 4$ red cars, $\small 8$ white cars and $\small 4$ yellow car, what is the probability that he will pick up a white car?

Answer

First we must determine how many toy cars Brian has in the box by adding them together.

$\small \small 3+4+8+4=19$

We know from the information provided that there are $\small 8$ white cars in the box, so the probability of Brian picking up one white car from the $\small 19$ possible cars is $\small \frac{8}{19}$ .

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Question

Express the probability as a percent, rounded to the nearest whole number.

Matt had a bag of 28 colored candies. If he had 6 red, 5 purple, 7 orange, and 10 yellow, what is the probability that he pulls out a red-colored candy?

Answer

Since there are 6 reds out of 28, divide $\frac{6}{28}=0.21428$ .

Move the decimal 2 places to the right 21.4% and round to the nearest whole number 21%.

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Question

Determine the probability of the outcome. Express the probability as a percent, rounded to the nearest whole number.

Erin saw a basket full of tiny bouncy balls. There were 27 green balls, 13 red balls, 11 yellow balls, and 13 spotted balls. What is the probability that Erin will choose a spotted ball or a yellow ball?

Answer

To find the probability of an outcome, set up a fraction: $\frac{part}{total, possible}$ .

Since there are 13 yellow balls PLUS 11 yellow balls (part) out of 64 balls in all (total possible) the fraction we can find what the fraction looks like.

$\frac{part}{total}=\frac{24}{64}$

If you reduce the fraction by 8 (because the numerator and the denominator are both divisible by 8), it can be simplified.

$\frac{24\div8}{63\div8}=\frac{3}{8}$

Since the question asks you to state the probability as a percent, we need to convert fraction to percent. We can set up a proportion.

$\frac{3}{8}=\frac{x}{100}$

Cross multiply and solve for $\small x$ .

$x=\frac{300}{8}=37.5$

This equals 37.5. Rounded to the nearest whole number gives us 38%.

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Question

Jessica has a pencil box with her favorite pencils and erasers. In the box there are different colored erasers. There are 4 pink, 3 blue, 10 yellow and 4 red erasers. What is the probability that Jessica will select an eraser from the box at random that is NOT red?

Answer

To find the probability of Jessica NOT picking a red eraser is the same as finding the probability that it is everything else that she wants.

First find the total number of erasers Jessica has by adding all of them no matter what the color may be. These are all the options whether she wanted them or not. In total there are total erasers.

Then count all of the erasers that are NOT red. That would be erasers that are NOT red.

The probability would be set up as:

$\frac{WANT - what, you , want , to , happen}{HAVE - everything , that , could , happen}$

So, you would have

$\frac{17}{21}$

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Question

A card is chosen at random from a standard deck of fifty-two cards. What is the probability that the card will be a queen or a heart, but not both?

Answer

Out of fifty-two cards, there are thirteen hearts, but since we are excluding the queen, this makes twelve cards that we are including. Out of the four queens, we include three of them - again, excluding the queen of hearts. This makes fifteen cards out of fifty-two, so the probability of drawing one of them is $\frac{15}{52}$ .

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Question

A card is chosen at random from a standard deck of fifty-two cards. What is the probability that the card will be a king, a spade, or both?

Answer

Out of fifty-two cards, there are thirteen spades; also, there are four kings, but one is a spade, so this makes three additional cards for a total of sixteen. The probability of drawing a card that is a king and/or a spade is therefore sixteen out of fifty-two, or:

$\frac{16}{52} = \frac{4}{13}$

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Question

A bag contains one token for every multiple of 6 from 1-90 (inclusive). If you draw out one token at random, what are the odds of it being a multiple of 4?

Answer

The simplest way to solve this is to make a chart of all of the multiples of 6 (just count by 6) from 1-90:

6 12 18 24 30

36 42 48 54 60

66 72 78 84 90

That makes 15 numbers, which will be our denominator.

Next, look through the list and identify the numbers that are divisible by 4 (divisible by 2, and then 2 again).

6 12 18 24 30

36 42 48 54 60

66 72 78 84 90

That is 7 numbers. Thus, $\frac{7}{15}$ of these multiples of 6 are also divisible by 4.

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Question

Marcus has a box of 24 crayons. 8 are blue, 6 are green, 4 are red, 3 are black, 2 are white, and 1 is purple. If he randomly picks a crayon from the box, which color has a 1 out of 6 chance of being chosen?

Answer

Red here is the correct answer. Marcus has a 4 out of 24 chance of choosing red, as there are 4 red crayons in a box of 24. Reduce the probability, and you get 1 out of 6.

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Question

Use the diagram to answer the question.

If one of the shapes is chosen at random, what is the probability that it is a black circle?

Answer

To find the probability, we use a fraction:

$\frac{part}{total}$

There are 12 total shapes, and 2 black circles:

$\frac{2}{12}$

Reduce:

$\frac{1}{6}$

Thus, the probability is 1 out of 6.

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Question

Susan has a bag of 12 assorted candies that included 3 blue, 2 green, 5 red, and 2 pink. If Susan picks one piece of candy without looking, what are the chances that she picks a blue candy?

Answer

To fine the chance of Susan picking a blue candy, consider how many blue candies there are: 3

Compared to how many candies there are total: 12

That means the chance of Susan picking a blue candy is $\frac{3}{12}$ , which simplifies to $\frac{1}{4}$ .

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Question

In a cupboard there are mugs, glasses and plastic cups. If someone randomly reaches into the cupboard and grabs one of these items, what is the probability that he or she will pull out a mug?

Answer

To write probability as a fraction, put the number of things that match what you're looking for in the numerator and the total number of things in the denominator. In this case, what we're looking for is mugs. There are mugs, so we'll put in the numerator. The total number of things in the cupboard is mugs glasses cups. , so we'll put in the denominator. This gives us $\small \frac{3}{12}$ , which we can simplify to $\small \frac{1}{4}$ . The correct answer is $\small \frac{1}{4}$ .

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Question

Susie has a normal 6-sided die. What is the probability of her rolling a 2?

Answer

Probability is a proportion of the number of incidences of a specific outcome (in this case rolling a 2- which can happen only once) divided by the total number of outcomes (in this case there are 6 outcomes- Susie can roll a 1, 2, 3, 4, 5, or 6).

$P=\frac{specific\ outcome}{total\ number\ of\ possible\ outcomes}=\frac{1}{6}$

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Question

A bag contains 12 black marbles, 4 blue marbles, and 8 red marbles. What is the probability of choosing a black marble?

Answer

Probability is defined as the number of opportunities for a specific outcome (in this instance the number of black marbles) divided by the total number of outcomes (total number of marbles).

$P=\frac{number\ of\ black\ marbles}{total\ number\ of\ marbles}=\frac{12}{12+4+8}=\frac{12}{24}=\frac{1}{2}$

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Question

What is the probability of flipping a coin 3 times and landing on heads all 3 times?

Answer

The probability of flipping a coin and having it land on heads one time is . The probability of multiple independent events can be found by multiplying the probabilities together. Independent events are events that do not influence the outcome of each other.

$P=\frac{1}{2}\times\frac{1}{2}\times\frac{1}{2}=\frac{1\times1\times1}{2\times2\times2}=\frac{1}{8}$

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Question

A single die is rolled. What is the probability of rolling greater than a 4?

Answer

There are 6 possible outcomes when rolling a die. There are 2 possible outcomes that are greater than 4 (5 and 6).

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

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Question

When flipping a fair coin three times, what is the probability of getting EXACTLY ONE head?

Answer

Let heads and tails.

Draw out the sample space:

The desired outcomes are:

Probability is a fraction between and , where the numerator is the number of desired outcomes and the denominator is the total number of outcomes.

Therefore the probability of getting exactly one head is $\frac{3}{8}$ .

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Question

When drawing two cards from a standard deck of playing cards, what is the probability of picking a red card followed by a black card if there is no replacement?

Answer

For a standard deck of cards:

So the probability of picking red then black without replacement is given by:

$\frac{26}{52}\cdot \frac{26}{51}=\frac{13}{51}$

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Question

When rolling two fair six-sided dice, what is the probability of getting more than eight?

Answer

More than means .

There are possible outcomes when rolling two six-sided dice.

The desired outcomes are:

This is a total of desired outcomes.

Probability is a fraction between and , where the numerator is the number of desired outcomes and the denominator is the total number of outcomes.

Therefore the probability is $\frac{10}{36}=\frac{5}{18}$ .

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