ACT Math : Probability
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Example Questions
Example Question #21 : Probability
There are 20 balls in a box, 10 are green, 5 are blue, and 5 are red. One red and one green ball are then removed from the box.
What is the probability that the third ball removed from the box will be green?
Not enough information given
This is a probability question, in the beginning, the odds of pulling a green ball were 10/20, which reduces down to 1/2. When 2 balls are removed, the total is now 18, and because there are only 9 green balls, we have a 9/18 chance of pulling a green ball, and this reduces down to 1/2
Example Question #22 : Probability
What is the probability that Jim flips a fair coin 3 times and gets 3 heads?
The probability of getting heads on one flip of a coin is 1/2, since the only other outcome is tails. Because the flips are independent of each other (one outcome does not depend on the others), the probability of the second coin being heads is 1/2 and the probability of the third coin being heads is 1/2. However, to calculate the probability of obtaining all of the flips ending in heads, we multiply the probabilities of the events together: (1/2)*(1/2)*(1/2) = 1/8.
Example Question #131 : Data Analysis
There is a box with 24 handkerchiefs, some are blue, some are red, and some are green.
If there are 4 red handkerchiefs in the box, and the probability of pulling a blue handkerchief is 3 times more likely than pulling a red one, what is the probability of pulling a green handkerchief?
If the probability of pulling out a blue handkerchief is 3 times that of pulling a red one, then it means there are 3 times as many blue handkerchiefs as there are red.
4 x 3 =12 blue handkerchiefs.
24 total – 12 blue – 4 red = 8 green handkerchiefs
8/24 simplifies into 1/3 (divide both numbers by 8)
Example Question #23 : Probability
There is a box with 24 handkerchiefs, some are blue, some are red, and some are green.
If there are 4 red handkerchiefs in the box, and the probability of pulling a blue handkerchief is 3 times more likely than pulling a red one, how many green handkerchiefs are in the box?
5
8
10
6
4
8
If the probability of pulling out a blue handkerchief is 3 times that of pulling a red one, then it means there are 3 times as many blue handkerchiefs as there are red.
4 x 3 =12 blue handkerchiefs.
24 total – 12 blue – 4 red = 8 green handkerchiefs
Example Question #23 : Probability
You roll two dice. The first die shows a 3 and the other die rolls under the table and you cannot see it. What is the probability that both die show 3 ?
1/3
1/6
9/36
5/6
1/36
1/6
A die has six sides and you already know that the first die shows the number 3. There is is a 1/6 probability that the second die under the table shows a 3.
Example Question #21 : How To Find The Probability Of An Outcome
Elena took a math test with 15 questions, each question having four choices. Elena is sure that she got exactly 9 of the first 12 questions correct, but she guessed randomly on the last 3 questions. What is the probability that she will get at least 80% on the test?
To get 80%, Elena needs to get 12 out of the 15 questions right. If she answered 9 out of the first 12 questions right, she can score 80% only if she guessed all 3 of the remaining questions correctly.
Therefore Elena has a (1/4)^3 chance of getting all 3 questions correct.
Example Question #24 : Probability
Robert has a lot of loose change in his pocket. He pulled it all out and found that he had 5 nickels, 8 dimes, 3 quarters, and 13 pennies in his pocket. Robert then put all the change back in his pocket except for the quarters. What is the probability of Robert pulling out a dime at random? (assume that the physical size of the coins has no effect on their probability of being picked)
1/13
1/26
8/29
13/26
4/13
4/13
The total number of coins in Robert's pocket is 26. because there are 8 dimes, he has an 8/26 chance of choosing a dime. This reduces down to 4/13 when you divide the numerator and denominator by 2 (GCF)
Example Question #25 : Probability
If there are 490 marbles in a bag, divided evenly into the seven colors of the rainbow, what is the probability of picking out a marble that is one of the three primary colors?
Since the rainbow consists of seven colors, and there are 490 marble, there are 70 of each color (490/7 = 70).
The probability of choosing a marble that is a primary color would be (70 * 3)/490 = 210/490 = 3/7.
Example Question #26 : Probability
A bottle contains 7 yellow jelly beans, 8 blue jelly beans, 9 green jelly beans, and 14 purple jelly beans. If you select one jelly bean at random, what is the probability that it is neither purple nor yellow? Round to the nearest hundredth.
0.45
0.57
0.76
0.43
0.87
0.45
This is a probability question. There are 17 jelly beans that could be selected to satisfy the conditions of selecting a jelly bean that is neither purple or yellow. There are 38 total jelly beans. The proportion should be set up as 17/38 or 0.45, because this represents the probability that a jelly bean that is not purple or yellow will be selected.
Example Question #27 : Probability
What is the probability of rolling a sum of four or less on a pair of regular six-sided dice?
1/2
1/6
1/3
1/4
1/12
1/6
Probability = what you want ÷ total number
There are 6 ways to get a sum of four or less: (1, 1), (1, 2), (1, 3), (2, 1), (2, 2), (3, 1)
The total would be 6 * 6 = 36
So the probability of getting four or less (4, 3, 2, 1) is 6/36 = 1/6
The probability of getting less than four (3, 2, 1) is 3/36 = 1/12
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