SSAT Elementary Level Quantitative - How to find the probability of an outcome

Malcolm is on vacation with his family. He packed five shirts and five pairs of shorts. There are three white shirts, one black shirt, and one blue shirt. There are two blue pairs of shorts, one yellow pair of shorts, one black pair of shorts, and one red pair of shorts. If Malcolm reached into his suitcase and pulled out an article of clothing, what is the probability that it is either blue or black?

$50% \textup{ chance}$

$40% \textup{ chance}$

$10% \textup{ chance}$

$60% \textup{ chance}$

$100% \textup{ chance}$

Explanation

We know that there are 10 articles of clothing (5 shirts and 5 pairs of shorts). First, you need to determine how many of these shirts and shorts are either blue or black. The problem says Malcolm has one black shirt, one blue shirt, two blue pairs of shorts, and one black pair of shorts.

$1\dotplus 1+2+1=5 \textup{ pairs of blue or black shorts}$

This means he has a 5 in 10 chance of picking clothing that is blue or black.

$\frac{5}{10} = 50%$

Find the probability of drawing a 3 from a deck of cards.

$\frac{1}{13}$

$\frac{1}{4}$

$\frac{4}{13}$

$\frac{1}{52}$

Explanation

To find the probability of an event, we will use the following formula:

$\text{probability of event} = \frac{\text{number of ways event can happen}}{\text{total number of possible outcomes}}$

So, given the event of drawing a 3, we can calculate the following:

\text{number of ways event can happen} = 4

Because there are 4 ways we can draw a 3 from the deck:

3 of clubs
3 of spades
3 of diamonds
3 of hearts

Now, we can calculate the following:

\text{total number of possible outcomes} = 52

Because there are 52 cards we could potentially draw from a deck of cards.

Knowing this, we can substitute into the formula. We get

$\text{probability of drawing a 3} = \frac{4}{52}$

$\text{probability of drawing a 3} = \frac{2}{26}$

$\text{probability of drawing a 3} = \frac{1}{13}$

Therefore, the probability of drawing a 3 from a deck of cards is $\frac{1}{13}$ .

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.

Ethan has a bag with 20 of his favorite marbles. He has 5 blue marbles, 7 red marbles, 2 white ones, 4 black ones, and 2 multi-colored marbles. What is the probability that he randomly picks a red marble out of the bag?

$\frac{7}{20}$

$\frac{1}{4}$

$\frac{1}{10}$

$\frac{1}{5}$

Explanation

The probability is expressed as the circumstance out of the whole number available.

The number of marbles that are red is 7, and the whole number of marbles is 20.

Therefore the probability is

$\frac{7}{20}$ .

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.

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

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 $\frac{1}{4}$ .

Ten cards each have a number printed on them. Five have a 1 printed on them, three have a 2, and two have a 3. The cards are shuffled and a card is dealt. What is the probability that the card will not be a 3?

$\frac{4}{5}$

$\frac{2}{5}$

$\frac{3}{10}$

$\frac{1}{3}$

$\frac{2}{3}$

Explanation

There are ten cards total, and eight cards that are not threes. This makes the probability of drawing a three

$\frac{8}{10} = \frac{4}{5}$

Mikey has a box filled with cookies. He has 6 chocolate chip cookies, 4 sugar cookies, and 2 oatmeal raisin cookies. What is the chance that Mikey picks a sugar cookie out of the box?

$\frac{4}{12}$

$\frac{2}{12}$

$\frac{1}{8}$

$\frac{4}{5}$

$\frac{6}{12}$

Explanation

To find the probability of picking a sugar cookie from the bag of cookies, we need to set up a fraction like this:

$\frac{sugar\ cookies}{total\ cookies}$

The problem tells us that Mikey has 4 sugar cookies, so we can put that on the top of the fraction. The total number of cookies is equal to 6 chocolate chip cookies + 4 sugar cookies + 2 oatmeal raisin cookies, giving us a sum of 12 (which goes on the bottom of the fraction). That gives Mikey a $\frac{4}{12}$ chance of picking a sugar cookie!