PSAT Math : Data Analysis
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Example Question #182 : Data Analysis
Two dice are rolled. What is the probability that the product of the numbers rolled is 15?
1/4
1/36
1/18
1/9
1/6
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 #111 : Statistics
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?
24/169
2/13
18/169
4/13
3/26
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 #184 : Data Analysis
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?
10
40
18
25
36
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 #185 : Data Analysis
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?
2/3
3/5
1/5
1/15
6/7
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 #141 : Data Analysis
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?
11/850
43/250
21/500
13/750
57/1000
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 #145 : Outcomes
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?
2/7
3/5
1/100
3/14
4/9
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
Example Question #22 : Probability
A number between 1 and 15 is selected at random. What are the odds the number selected is a multiple of 6?
2/15
The answer is not listed
1/7
3/15
3/7
2/15
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 #141 : Data Analysis
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?
2/7
3/7
5/12
7/12
1/3
5/12
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 #21 : How To Find The Probability Of An Outcome
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?
3/400
3/200
5/200
1/200
1/100
1/200
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 #21 : 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?
1/36
2/9
1/72
1/8
1/6
1/36
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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