SAT Math : How to find the probability of an outcome

Study concepts, example questions & explanations for SAT Math

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Example Questions

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

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:

13

20

22

16

18

Correct answer:

20

Explanation:

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 #22 : 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:

1/18

1/36

1/9

1/4

1/6

Correct answer:

1/18

Explanation:

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 #23 : 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:

3/26

4/13

18/169

24/169

2/13

Correct answer:

2/13

Explanation:

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 #24 : Probability

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:

10

18

36

25

40

Correct answer:

36

Explanation:

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 #25 : Probability

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

1/5

1/15

6/7

2/3

Correct answer:

1/15

Explanation:

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 #26 : Probability

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

21/500

13/750

57/1000

11/850

Correct answer:

11/850

Explanation:

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 #27 : Probability

A number between 1 and 15 is selected at random.  What are the odds the number selected is a multiple of 6?

Possible Answers:

The answer is not listed

1/7

3/15

3/7

2/15

Correct answer:

2/15

Explanation:

In the set of 1 to 15, two numbers, 6 and 12, are multiples of 6. That means there are two chances out of 15 to select a multiple of 6.

2/15

Example Question #28 : Probability

A big box of crayons contains a total of 120 crayons. 

The box is composed of 3 colors; red, blue, and orange. 30 of the crayons are red, 40 of the crayons are blue and the rest are orange. If one picks a crayon randomly from the box, what is the probability that it will be orange? 

Possible Answers:

3/7 

7/12

2/7 

1/3 

5/12

Correct answer:

5/12

Explanation:

To solve the problem one must calculate that there are 50 orange crayons in the box. So 50/120 are orange. If we simplify that fraction by 10 we get 5/12.

Example Question #29 : Probability

A skydiver is trying to determine the probability of landing within the target of a grass field. If the field measures 1000 meters by 500 meters and the target area measures 50 meters by 50 meters, what is the probability of the skydiver landing in the target area?

Possible Answers:

1/200

1/100

3/400

5/200

3/200

Correct answer:

1/200

Explanation:

Find the area of the entire field and the target area. The fraction of the field that is the target area is equal to the probability of the skydiver hitting the target area. For example, if the field were 100 m3 and the target area was 100 m3 than the probability would be 1. If the field were 100 m3 and the target area was 50 m3 than the probability would be 0.5 and so on.

(50 * 50)/(1000 * 500) = 5/1000 = 1/200

Example Question #30 : Probability

If a container holds 4 red balls, 3 yellow balls, and 2 blue balls, what are the odds of picking out both of the blue balls without replacement?

Possible Answers:

1/8

1/72

1/36

2/9

1/6

Correct answer:

1/36

Explanation:

You take the probability of the first outcome times the probability of the second, so (2/9) * (1/8) = 2/72 = 1/36

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