ISEE Lower Level Quantitative Reasoning - Probability

Joey has 10 shirts on his bed. 4 shirts are blue, 3 shirts are purple, 2 shirts are green, and 1 shirt is white. What is the chance that Joey randomly picks a purple shirt from the shirts on his bed?

$\frac{3}{10}$

$\frac{3}{4}$

$\frac{2}{10}$

$\frac{1}{5}$

$\frac{3}{8}$

Explanation

To find the probability of picking a purple shirt from the pile of shirts on Joey's bed, we need to set up a fraction like this:

$\frac{purple\ shirts}{total\ shirts}$

The problem tells us that Joey has 3 purple shirts, so we can put that in the numerator. We are also told that the total number of shirts on Joey's bed is 10, so 10 goes on the bottom of the fraction. Therefore, Joey has a $\frac{3}{10}$ chance of picking a purple shirt.

A jar contains candy bars, lollipops, and other types of sweets. What is the probability of drawing a lollipop at random from the jar?

$\frac{1}{5}$

$\frac{3}{10}$

$\frac{1}{2}$

$\frac{2}{5}$

Explanation

Probability can be expressed as a fraction. The numerator represents the total number of what is being chosen and the denominator represents the total number of items that can be chosen. In this problem, there are lollipops and a total of pieces of candy. This is represented as the fraction: $\tfrac{2}{10}$ . This can be reduced to $\tfrac{1}{5}$ . The answer is $\tfrac{1}{5}$ .

Harvey has a bouquet of 12 flowers: 5 are lilacs, 3 are roses, 2 are orchids, and 2 are dandelions. What is the chance that Harvey randomly selects a rose from the bouquet?

$\frac{1}{4}$

$\frac{3}{15}$

$\frac{2}{12}$

$\frac{1}{3}$

$\frac{7}{12}$

Explanation

To find the probability of Harvey picking a rose from the bouquet of flowers, we need to set up a fraction like this:

$\frac{roses}{total\ flowers}$

The problem tells us that Harvey has 3 roses, so we can put that on the top of the fraction. The problem also tells us that Harvey has 12 total flowers, so we can put that on the bottom of the fraction. That gives Harvey a $\frac{3}{12}$ chance of picking a rose from the bouquet!

Since $\frac{3}{12}$ is not an answer choice, we need to reduce the fraction. To reduce a fraction means to divide the top (numerator) and the bottom (denominator) by a common factor that both numbers share. The numbers 3 and 12 both have a common factor of 3, so we can divide the top and the bottom by 3 to get the correct answer of $\frac{1}{4}$ .

Caroline has 3 books, 2 pencils, 1 candy, and 4 binders in her backpack. If she randomly chooses an item from her backpack, what is the probability of her randomly picking out a pencil?

$\frac{1}{}5$

$\frac{1}{10}$

$\frac{3}{10}$

$\frac{2}{5}$

Explanation

Probability is all about part and whole. First, add up how many items are in her backpack (10). Then, notice how many pencils she has (2). Put the part over the whole, which gives you $\frac{2}{10}$ .

This can be further simplified/reduced to $\frac{1}{5}$ .

Selena has a standard deck of cards. What is the chance that she randomly selects a red card from the deck?

$\frac{1}{2}$

$\frac{1}{13}$

$\frac{2}{7}$

$\frac{1}{4}$

$\frac{3}{4}$

Explanation

To find the probability of Selena picking a red card from a standard deck of cards, we need to set up a fraction like this: $\frac{\text{red cards}}{\text{total cards}}$ .

A standard deck of cards has 52 cards, 26 of which are black and 26 of which are red. Our fraction looks like this:

$\frac{\text{red cards}}{\text{total cards}}=\frac{26}{52}$

We can reduce the fraction, since both numbers share a common factor.

$\frac{26}{52}=\frac{26\div26}{52\div26}=\frac{1}{2}$

There are 2 blue blocks, 3 red blocks, and some yellow blocks on the ground. If the probability of picking a red block is $\frac{3}{10}$ , how many yellow blocks are there?

Explanation

The probability given in the problem tells us how many total blocks there are, which is 10. (Probability is part over whole.) Since we know that there are 10 total, we can subtract the quantities of the red and blue blocks:

Therefore there are 5 yellow blocks.

A store has a bin of books on sale. In the bin, there are novels, comic books, reference books, and picture books. What is the probability that someone will choose a novel from the bin?

$\frac{2}{5}$

${}\frac{1}{10}$

$\frac{1}{5}$

$\frac{1}{2}$

Explanation

Probability can be expressed as a fraction. The numerator represents the total number of what is being chosen and the denominator represents the total number of items that can be chosen. In this problem, there are novels and a total of books. This is represented as the fraction: $\tfrac{10}{25}$ . This can be reduced to $\tfrac{2}{5}$ . The answer is $\tfrac{2}{5}$ .

A bag contains differently colored balls. In it are pink balls, red balls, and green balls. What is the probability of choosing a red ball at random?

$\frac{2}{5}$

$\frac{1}{5}$

$\frac{1}{3}$

$\frac{2}{3}$

Explanation

Probability can be expressed as a fraction. The numerator represents the total number of what is being chosen and the denominator represents the total number of items that can be chosen. In this problem, there are red balls and a total of balls in the bag. This is represented as the fraction: $\tfrac{6}{15}$ . This can be reduced to $\tfrac{2}{5}$ . The answer is $\tfrac{2}{5}$ .

Ebony has a drawer of socks with five different colors: green, purple, black, white, and yellow. The probability of her choosing a white sock is 3 out of 7. Which combination of socks is possible?

6 white socks and 14 other socks

3 white socks and 7 other socks

7 white socks and 21 other socks

9 white socks and 12 other socks

1 white sock and 4 other socks

Explanation

We are looking at probability and proportion in this problem.

If there is a 3 out of 7 chance of getting a white sock, this can be expressed as $\frac{3}{7}$ or 3:7.

Then, we must find an equivalent combination, which would be 6:14.

There are marbles in a bag: are blue, are white, are yellow, and are green. What is the probability of choosing blue or green at random?

$\frac{2}{5}$

$\frac{1}{2}$

$\frac{3}{10}$

${}\frac{2}{10}$

Explanation

Probability can be expressed as a fraction. The numerator represents the total number of what is being chosen and the denominator represents the total number of items that can be chosen. In this problem, there are blue and green marbles and a total of chocolates. This is represented as the fraction: $\tfrac{4}{10}$ . This can be reduced to $\tfrac{2}{5}$ . The answer is $\tfrac{2}{5}$ .

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