### All PSAT Math Resources

## Example Questions

### Example Question #12 : Probability

A coin is flipped 4 times. What is the probability of getting 4 heads in a row?

**Possible Answers:**

**Correct answer:**1/16

The probability a heads will show on any flip is 1/2. To find the probability of 4 consecutive heads, multiply the probability of each individual flip together.

1/2 * 1/2 * 1/2 * 1/2 = 1/16

### Example Question #11 : Probability

A restaurant offers two different entrees, four different side dishes, and three desserts. If a customer wants to order a meal special that consists of one entree, two different side dishes, and one dessert, how many different meals are possible?

**Possible Answers:**

**Correct answer:**36

Our strategy is as follows: We must determine the number of possible entrees, the number of possible combinations of two side dishes, and the number of desserts. Then we must multiply these four numbers together to get the number of all of the possible meals.

Let's label the two different entrees E_{1} and E_{2} The customer can choose one of these, so he has two different options for his entree.

Let's label the four different side dishes S_{1}, S_{2}, S_{3}, and S_{4}. The customer can only choose two of these four dishes, and the order in which he chooses doesn't matter. For example, if he were to choose mashed potatoes and broccoili, he would end up with the same meal as if he were to choose broccoli and then mashed potatoes. So we need to consider all of the different pairs that can be selected from these four side dishes. Here are all of the possible combinations:

S_{1 }and S_{2}

S_{1 }and S_{3}

S_{1 }and S_{4}

S_{2} and S_{3}

S_{2} and S_{4}

S_{3} and S_{4}

This means that the customer has six different combinations of two side dishes.

Finally, the customer can choose one dessert from three different choices. This means there are three possibilities for dessert.

So, the customer has two different options for entrees, six different options for the two side dishes, and three different choices for dessert. To find the total number of meals possible, we can multiply these three numbers together.

Number of meals = 2 x 6 x 3 = 36.

The answer is 36.

### Example Question #11 : How To Find The Probability Of An Outcome

How many positive four-digit integers have the thousands digit equal to 8 and the units digit (ones digit) equal to 5?

**Possible Answers:**

20

99

200

100

10

**Correct answer:**

100

The number of possibilities in a joint event (that is, the entire four-digit integer) is the product of the number of possibilities of each individual event (the number of possibilities for each digit individually). If WXYZ represents a 4-digit integer, the problem tells us that there is only one possible value for W (which is 8) and only possible value for Z (which is 5). We also know that there are ten possibilities each for X and Y (they can be the digits 0-9). So the number of possible values for WXYZ is the product of the possible values for each digit, which is 1 * 10 * 10 * 1 = 100.

### Example Question #21 : Probability

Nora is packing for a trip. Of the scarves in her closet, 8 are blue. She will randomly pick one of the scarves to pack. If the probability is 2/5 that the scarf she will pick is blue, how many scarves are in her closet?

**Possible Answers:**

16

18

13

20

22

**Correct answer:**

20

We are told that there are 8 blue scarves in the closet, and that the probability of a blue scarf being chosen is 2/5. So, if T represents the total scarves in the closet, we know that 8/T = 2/5.

Cross-multiplying gives:

40 = 2T

And dividing both sides by 2 gives:

20 = T

Therefore, Nora has a total of 20 scarves in her closet.

### Example Question #21 : How To Find The Probability Of An Outcome

Two dice are rolled. What is the probability that the product of the numbers rolled is 15?

**Possible Answers:**

1/4

1/36

1/6

1/9

1/18

**Correct answer:**

1/18

The only possibility to roll a product of 15 is to roll a 5 on the first dice and a 3 on the other, or a 3 on the first and 5 on the second. There are 36 total possibilities for two dice (6 * 6), 2 possibilities out of 36 gives you 2/36 = 1/18.

### Example Question #21 : Probability

A jar contains three red marbles, four blue marbles, and six green marbles. Jennifer draws a marble and then draws a second one without replacement. What is the probability that she will draw a blue marble and then a green marble?

**Possible Answers:**

18/169

3/26

24/169

2/13

4/13

**Correct answer:**

2/13

There are three red marbles, four blue marbles, and six green marbles. This means that there are a total of thirteen marbles.

The probability of drawing a blue marble on the first drawy would be 4/13.

Because Jennifer doesn't replace the marble, after she draws the blue marble, there are only twelve marbles left. This means that the probability of next drawing a green marble would be 6/12 = 1/2.

To find the probability of the two events happening together, we must multiply them. In general, when you want to find the probability of one event AND another, you must multiply.

probability = (4/13)(1/2) = 2/13

The answer is 2/13.

### Example Question #21 : How To Find The Probability Of An Outcome

The Sugar Shak has a "make your own sundae" bar. You can choose one of three ice creams (strawberry, chocolate, or vanilla), one of three sauces (strawberry, carmel, or chocolate), and one of four toppings (peanuts, whipped cream, cherry, or M&Ms). How many different sundaes can be made?

**Possible Answers:**

18

25

36

40

10

**Correct answer:**

36

We have three choices for ice cream, three choices for sauces, and four choices for toppings. Each selection is an independent event, so the choices are multiplied together: 3 * 3 * 4 = 36.

### Example Question #21 : How To Find The Probability Of An Outcome

A bag contains two white marbles, five green marbles, and three red marbles. What is the probability of picking two red marbles if replacement is not allowed?

**Possible Answers:**

3/5

6/7

2/3

1/5

1/15

**Correct answer:**

1/15

Probability is a number between 0 (will not happen) and 1 (will definitely happen). Probability is generally a fraction where the numerator is the total of what you want to happen and the denominator is the total count.

Total ways to choose two red marbles: 3 * 2 = 6

Total ways to choose two marbles: 10 * 9 = 90

Therefore, the probability of choosing two red marbles is 6/90 or 1/15

### Example Question #21 : How To Find The Probability Of An Outcome

What is the probability of choosing three hearts in three draws from a standard deck of playing cards, if replacement of cards is not allowed?

**Possible Answers:**

43/250

13/750

21/500

57/1000

11/850

**Correct answer:**

11/850

The standard deck of cards has 52 cards: 13 cards in 4 suits.

Ways to choose three hearts: 13 * 12 * 11 = 1716

Ways to choose three cards: 52 * 51 * 50 = 132600

Probability is a number between 0 and 1 that is defines as the total ways of what you want ÷ by the total ways

The resulting simplified fraction is 11/850

### Example Question #141 : Probability

A lottery is being run at a high school to allocate parking spots. The school has 200 seniors, 300 juniors, 350 sophomores, and 450 freshmen. Each eligible senior will have their name entereted into the lottery twice, with all other eligible students' names being entered once. Only juniors and seniors will be eligible for parking spots. If there are 150 parking spots, what is the probability that any given junior will receive a spot?

**Possible Answers:**

3/14

4/9

1/100

3/5

2/7

**Correct answer:**

3/14

Find the probabilty a junior's name will be pulled for a single lottery trial. Then calculate the probability given 150 lottery trials.

(200 seniors * 2 entries each) + 300 juniors = 700 entries

For any single junior then, the odds are 1/700 for a single lottery trial.

For 150 trials, a junior will have (1/700 * 150 trials) = 150/700, which simplifies to

3/14

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