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ACT Math : Probability

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Example Question #181 : Data Analysis

When drawing a single card from a deck of cards, what is the probability you draw a black card, or a two? Give your answer as a simplified fraction.

Possible Answers:

$\frac{1}{13}$

$\frac{2}{13}$

$\frac{1}{2}$

$\frac{7}{13}$

Correct answer:

$\frac{7}{13}$

Explanation:

To find the probability of an outcome, find the total number of ways that event can happen divided by the total number of possible outcomes.

There are 52 cards in a deck of cards, so there are 52 total possible outcomes. Of those, there are 26 black cards, and 4 twos.

However, of those 4 twos, two have already been included when we counted the 26 black cards (the 2 of clubs and 2 of spades), thus there are only two additional twos to add to our total of 26 black cards.

This yields 28 possibilities, which when divided by 52 reduces to:

$\frac{7}{13}$

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Example Question #71 : How To Find The Probability Of An Outcome

What is the probability of drawing a face card from a standard, 52 card deck of cards? Give your answer as a reduced fraction.

Possible Answers:

$\frac{1}{52}$

$\frac{3}{13}$

$\frac{12}{52}$

$\frac{4}{52}$

$\frac{1}{13}$

Correct answer:

$\frac{3}{13}$

Explanation:

To find the probability of an event, determine the number of ways the event can happen, and divide that by the total number of possible outcomes.

Because there are 52 cards in a deck of cards, the total possible number of outcomes is 52.

Since there are 3 face cards (Jack, Queen, King) and four suits, there are a total of 12 face cards.

$\frac{12}{52} = \frac{3}{13}$

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Example Question #71 : Outcomes

When rolling at $\textup{15-sided}$ die, what is the probability that you roll a number greater than ? Give your answer as a reduced fraction.

Possible Answers:

$\frac{11}{15}$

$\frac{1}{3}$

$\frac{1}{15}$

$\frac{7}{15}$

$\frac{4}{15}$

Correct answer:

$\frac{4}{15}$

Explanation:

To find the probability of an outcome figure out the number of ways the specified event can occur (rolling a number greater than ), divided by the total number of outcomes. Since there are possible numbers to roll, the total number of outcomes is . The numbers greater than are: $\textup{12, 13, 14, 15}$ for a total of possibilities. Thus the answer is:

$\frac{4}{15}$ .
(Note, is not included in "greater than", if it said "greater than or equal to " it would be).

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Example Question #184 : Data Analysis

When rolling a $\textup{6-sided}$ die, what is the probability you roll a number less than or equal to ? Give your answer as a reduced fraction.

Possible Answers:

$\frac{2}{6}$

$\frac{1}{2}$

$\frac{3}{6}$

$\frac{1}{3}$

$\frac{1}{6}$

Correct answer:

$\frac{1}{3}$

Explanation:

To find the probability of an event, find out how many ways that specific event can happen and divide it by the total number of possible outcomes. The only numbers less than or equal to on a sided die are and . There are possible outcomes. Thus the reduced fraction is:

$\frac{1}{3}$

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Example Question #71 : Probability

Aaron flips a fair coin 7 times. The outcomes are shown below, in the order of the coin flips. H denotes heads, T denotes tails. Which outcome is most unlikely?

I) HHHHHHH

II) TTTTTTH

III)THHTHTT

Possible Answers:

III

I and II

They are equally unlikely.

Correct answer:

They are equally unlikely.

Explanation:

Even though I and II may seem like rarer outcomes, all of the answer choices have an equal probability of occurring, as the probability for each outcome is 0.50 in each flip and the probability for each of these sequences of coin flips equals (0.50)^7.

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Example Question #72 : Probability

If you roll a six-sided die, what is the probability of rolling a prime number?

Possible Answers:

$\frac{1}{6}$

$\frac{5}{6}$

$\frac{1}{3}$

$\frac{1}{2}$

$\frac{2}{3}$

Correct answer:

$\frac{1}{2}$

Explanation:

$2\textup{,}3\textup{, and }5$ are the prime numbers on a die, so since there are 6 sides the odds would be $\frac{3}{6}\textup{ or }\frac{1}{2}$ .

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Example Question #71 : How To Find The Probability Of An Outcome

Six lightning rods are set up around key buildings in an office complex. The odds of lightning striking any one of them are roughly equal, with a seventh option (equally likely as any of the others) being that the lightning strikes anything else instead, like a tree or plane.

What are the odds that the next three lightning strikes all hit different lightning rods?

Possible Answers:

$\frac{120}{343}$

$\frac{4}{21}$

$\frac{13}{121}$

$\frac{5}{7}$

$\frac{4}{7}$

Correct answer:

$\frac{120}{343}$

Explanation:

To calculate the odds of a chain of events, multiply the events' probabilities together. Since we want the lightning to strike any rod target on the first bolt, our odds of success are $\frac{6}{7}$ . The next bolt cannot hit the non-rod target nor the target that was already struck, so our chances are now $\frac{5}{7}$ . The last bolt cannot strike either of the previous two targets or the ground, so our odds drop further to $\frac{4}{7}$ . Multiply these individual probabilities to get the probability of this chain of events:

$\frac{6}{7} \cdot \frac{5}{7} \cdot \frac{4}{7} = \frac{120}{343}$

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Example Question #72 : How To Find The Probability Of An Outcome

The odds of guessing a question right on a particular test are $\frac{1}{5}$ . Connell guesses on all ten questions on the test, and gets a score of $30\%$ . What were the odds of this score?

Possible Answers:

$\frac{240}{2387}$

$\frac{16384}{9765625}$

$\frac{6535}{85749}$

$\frac{9998}{77031}$

$\frac{9687}{183860}$

Correct answer:

$\frac{16384}{9765625}$

Explanation:

To find the odds of a particular chain of outcomes, find the product of the odds of each required step's outcomes.

In this case, we can assume that Connell got the first three questions right (in other words, the order doesn't matter since it doesn't noticeably bias the later results).

So the odds of this are:

$\left(\frac{1}{5}\right)^3 = \frac{1}{125}$

The odds of getting a problem wrong with a blind guess, on the other hand, is $\frac{4}{5}$ , so the next seven questions being wrong have an odds of:

$\left(\frac{4}{5}\right)^7 = \frac{16384}{78125}$

Lastly, multiply our two individual probabilities together:

$\frac{1}{125} * \frac{16384}{78125} = \frac{16384}{9765625}$

Thus, the odds of getting this exact result are $\frac{16384}{9765625}$

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Example Question #73 : How To Find The Probability Of An Outcome

Jeremy has three coins. Each of the coins have a tails and heads side. If Jeremy flips all three coins, what is the probability that Jeremy gets tails on all three coins?

Possible Answers:

$\frac{1}{4}$

$\frac{1}{8}$

$\frac{1}{2}$

$\frac{1}{6}$

$\frac{1}{16}$

Correct answer:

$\frac{1}{8}$

Explanation:

This is a probability problem. What you must first decide is what is the probability of getting the outcome you want?

The probability of getting tails on each of the three coins is $50\%$ or $\frac{1}{2}$ .

Since we have three coins, we multiply their individual probabilities to get the final answer:

$\frac{1}{2}*\frac{1}{2}*\frac{1}{2} = \frac{1}{8}$ .

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Example Question #72 : Outcomes

In a bag, there are 5 green marbles, 8 blue marbles, and 7 red marbles. What is the probability of pulling out a blue marble.

Possible Answers:

$\frac{2}{5}$

$\frac{2}{3}$

$\frac{7}{20}$

$\frac{1}{4}$

Correct answer:

$\frac{2}{5}$

Explanation:

To find probability, you must take the # of desired outcomes divided by the total. Thus,

$P=\frac{8}{20}=\frac{2}{5}$

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ACT Math : Probability

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #181 : Data Analysis

Example Question #71 : How To Find The Probability Of An Outcome

Example Question #71 : Outcomes

Example Question #184 : Data Analysis

Example Question #71 : Probability

Example Question #72 : Probability

Example Question #71 : How To Find The Probability Of An Outcome

Example Question #72 : How To Find The Probability Of An Outcome

Example Question #73 : How To Find The Probability Of An Outcome

Example Question #72 : Outcomes

All ACT Math Resources

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