ACT Math : Probability
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Example Questions
Example Question #31 : How To Find The Probability Of An Outcome
If you flip a coin 3 times, what are the odds that the coin will be heads all three times?
If you flip a coin, the chances of you getting heads is 1/2. This is true every time you flip the coin so if you flip it 3 times, the chances of you getting heads every time is 1/2 * 1/2 * 1/2, or 1/8.
Example Question #31 : How To Find The Probability Of An Outcome
What is the probability of getting a sum of four when rolling two six-sided dice?
The sample space for rolling two six-sided dice 
There are three ways to roll a four.
The probability of rolling a four is given by the number of outcomes that produce a four divided by the total number of outcomes.
Example Question #31 : Outcomes
A bag contains 3 green marbles, 5 red marbles, and 9 blue marbles.
What is the probability of drawing a red marble?
The probability of drawing a red marble is 
The total number of marbles 
Example Question #31 : How To Find The Probability Of An Outcome
In a certain lottery, ten balls are numbered #1 through #10. Two winning balls will be drawn without replacement.
Billy plays the lottery and picks the numbers 9 and 10.
What is the probability Billy Bob will have two winning numbers?
1/90
1/50
1/100
1/45
2/95
1/90
(1/10)(1/9) = 1/90
Example Question #31 : How To Find The Probability Of An Outcome
In a lottery, ten balls are numbered #1 through #10. Two winning balls will be drawn without replacement.
Billy plays the lottery and picks the numbers 9 and 10.
What is the probability that Billy has no winning numbers? (Round to the nearest one percent.)
88%
92%
55%
96%
62%
62%
The correct answer is 62%, obtained from (8/10) (7/9) = 0.62222
Example Question #31 : How To Find The Probability Of An Outcome
A fair coin is tossed 2 times.
When flipping a coin twice, what is the probability of getting one heads and one tails? Without regard to order. I.e., either the heads or the tails could appear first.
1.0
0.75
0
0.5
0.25
0.5
There are 4 possible outcomes for the event {HH, HT, TH, TT}. Two of these four outcomes include exactly one heads and one tails.
Thus the solution is 2/4 = 1/2 = 0.5
Example Question #32 : Probability
With a pair of standard six-sided dice, what is the probability of getting a sum of less than five OR at least ten?
Probability is a fraction between 0 and 1. The denominator is the total number of possible outcomes and the numerator is the total number of desired outcomes. For two dice, the total number of ways to roll the dice is 36 (6 on the first die can go with any of the 6 on the second die)
The following outcomes result in a sum of less than 5: {1, 1} {1, 2} {1, 3} {2, 1} {2, 2} {3, 1}, for 6 possible outcomes
The following outcomes result in a sum of at least 10: {4, 6} {5, 6} {5, 5} {6, 6} {6, 5} {6, 4} for 6 possible outcomes
Since we are looking for a sum of less than five OR a sum of at least ten, we sum up the total number of desired outcomes
So the probability of getting less than five or at least ten will be 12/36, or 1/3
Example Question #31 : How To Find The Probability Of An Outcome
There are 6 pink marbles, 3 green marbles, and 5 white marbles in a bag; if one marble is taken out, what is the probability that the marble is pink?
There are 6 pink marbles out of 14 total, which reduces to 3/7.
Example Question #32 : How To Find The Probability Of An Outcome
A fair coin is flipped three times. What is the probability that the outcome is heads all three times?
There are 8 possible sequences that can occur given this scenario, listed as {HHH, HHT, HTT, HTH, THT, THH, TTH, TTT}
Only one element in this set is the desired outcome of 3 heads. So we get 1/8 is our probability.
Another way to look at this problem is to consider that the probability of flipping heads once is 1/2, so the probability of flipping heads 3 times consecutively is 1/2 * 1/2 * 1/2 = 1/8
Example Question #31 : How To Find The Probability Of An Outcome
A single die is rolled and one coin is flipped.
What is the probability of getting a number less than 4 on the die and a heads on the coin?
To get a number less than 4 on a die, 3/6 is the probability. To get a heads is a 1/2 chance.
So, since both events are independent, multiply the two probabilities together to get your answer.
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