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ISEE Lower Level Math : Probability

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Example Question #11 : How To Find The Probability Of An Outcome

Susie has a normal 6-sided die. What is the probability of her rolling a 2?

Possible Answers:

1/3

1/2

2/6

1/6

Correct answer:

1/6

Explanation:

Probability is a proportion of the number of incidences of a specific outcome (in this case rolling a 2- which can happen only once) divided by the total number of outcomes (in this case there are 6 outcomes- Susie can roll a 1, 2, 3, 4, 5, or 6).

$P=\frac{specific\ outcome}{total\ number\ of\ possible\ outcomes}=\frac{1}{6}$

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Example Question #12 : How To Find The Probability Of An Outcome

What is the probability of flipping a coin 3 times and landing on heads all 3 times?

Possible Answers:

1/8

1/2

3/2

1/6

Correct answer:

1/8

Explanation:

The probability of flipping a coin and having it land on heads one time is 1/2 . The probability of multiple independent events can be found by multiplying the probabilities together. Independent events are events that do not influence the outcome of each other.

$P=\frac{1}{2}\times\frac{1}{2}\times\frac{1}{2}=\frac{1\times1\times1}{2\times2\times2}=\frac{1}{8}$

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Example Question #13 : How To Find The Probability Of An Outcome

A single die is rolled. What is the probability of rolling greater than a 4?

Possible Answers:

$\frac{1}{2}$

$\frac{1}{3}$

$\frac{2}{3}$

$\frac{1}{6}$

Correct answer:

$\frac{1}{3}$

Explanation:

There are 6 possible outcomes when rolling a die. There are 2 possible outcomes that are greater than 4 (5 and 6).

$\frac{2}{6}=\frac{1}{3}$

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Example Question #11 : How To Find The Probability Of An Outcome

When rolling two fair, six-sided dice, what is the probability of getting at least one three?

Possible Answers:

$\frac{13}{18}$

$\frac{1}{3}$

$\frac{11}{36}$

$\frac{1}{6}$

$\frac{5}{9}$

Correct answer:

$\frac{11}{36}$

Explanation:

Probability is a fraction between and , where the numerator is the number of desired outcomes and the denominator is the total number of outcomes.

The sample space, or the total number of possible outcomes, for rolling two six-sided dice is .

To count up the desired outcomes consider three options:

1) the first dice has a three ( outcomes)

2) the second dice has a three ( outcomes)

3) both dice have a three ( outcomes)

So the total desired outcomes is 6+6-1=11 .

The subtraction is necessary because the intersection is counted twice, once for the first die and once for the second die.

Therefore the probability of rolling at least one three is $\frac{11}{36}$ .

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Example Question #15 : How To Find The Probability Of An Outcome

Given a deck of twenty-six alphabetical cards, what is the probability of picking a vowel and then a consonant without replacement?

Note: Y is considered a consonant.

Possible Answers:

$\frac{17}{169}$

$\frac{13}{150}$

$\frac{19}{120}$

$\frac{25}{144}$

$\frac{21}{130}$

Correct answer:

$\frac{21}{130}$

Explanation:

Probability is a fraction between and , where the numerator is the number of desired outcomes and the denominator is the total number of outcomes.

$26\; letters=5\; vowels+21\; consonants$

$\frac{5}{26}\cdot \frac{21}{25}=\frac{21}{130}$

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Example Question #11 : Data Analysis And Probability

The Malt Shoppe has a special on Build Your Own Sundae. They have chocolate, vanilla, and strawberry ice cream. In addition, they have hot fudge and caramel sauces, peanuts, whipped cream, M&Ms, and chocolate chips for toppings. If repetition is possible, how many different sundaes are possible if you choose two scoops of ice cream, one sauce, and two toppings?

Possible Answers:

144

480

320

288

164

Correct answer:

288

Explanation:

This is a counting problem where repetition is allowed.

Since there are three types of ice cream and you can choose two scoops, there are $3\cdot 3=9$ options for ice cream choices.

Since there are two types of sauces and you can choose one, there are $2\cdot 1=2$ options for sauces.

Since there are four types of toppings and you can choose two, there are $4\cdot 4=16$ options for topping.

Putting it all together, there are $9\cdot 2\cdot 16 = 288$ total sundae combinations.

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Example Question #17 : How To Find The Probability Of An Outcome

A family has three children. What is the probability that the middle and youngest children are both girls?

Possible Answers:

$\frac{1}{2}$

$\frac{5}{8}$

$\frac{1}{4}$

$\frac{3}{4}$

$\frac{3}{8}$

Correct answer:

$\frac{1}{4}$

Explanation:

Probability is a fraction between and , where the numerator is the number of desired outcomes and the denominator is the total number of outcomes.

The sample space, or the total possible outcomes, is .

There are two ways to have girls in the middle and youngest spots:

$BGG \; or\; GGG$

This probability is $\frac{2}{8}=\frac{1}{4}$ .

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Example Question #18 : How To Find The Probability Of An Outcome

When flipping a fair coin three times, what is the probability of getting EXACTLY ONE head?

Possible Answers:

$\frac{3}{8}$

$\frac{1}{2}$

$\frac{1}{3}$

$\frac{5}{8}$

$\frac{3}{4}$

Correct answer:

$\frac{3}{8}$

Explanation:

Let heads and tails.

Draw out the sample space:

$HHH\; \; \; \; \; HHT\; \; \; \; HTH\; \; \; \; HTT$

$TTT\; \; \; \; TTH\; \; \; \; THT\; \; \; \; THH$

The desired outcomes are:

$HTT\; \; \; \; THT\; \; \; \; TTH$

Probability is a fraction between and , where the numerator is the number of desired outcomes and the denominator is the total number of outcomes.

Therefore the probability of getting exactly one head is $\frac{3}{8}$ .

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Example Question #11 : How To Find The Probability Of An Outcome

When drawing two cards from a standard deck of playing cards, what is the probability of picking a red card followed by a black card if there is no replacement?

Possible Answers:

$\frac{19}{52}$

$\frac{17}{26}$

$\frac{13}{51}$

$\frac{13}{102}$

$\frac{19}{104}$

Correct answer:

$\frac{13}{51}$

Explanation:

For a standard deck of cards:

$52\; cards=26 \; red + 26\; black$

So the probability of picking red then black without replacement is given by:

$\frac{26}{52}\cdot \frac{26}{51}=\frac{13}{51}$

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Example Question #11 : Probability

When rolling two fair six-sided dice, what is the probability of getting more than eight?

Possible Answers:

$\frac{4}{9}$

$\frac{7}{18}$

$\frac{5}{12}$

$\frac{1}{4}$

$\frac{5}{18}$

Correct answer:

$\frac{5}{18}$

Explanation:

More than means 9,10,11, or 12 .

There are possible outcomes when rolling two six-sided dice.

The desired outcomes are:

$12:\; \; 6,6$

$11:\; \; 6,5\; \; \; \; 5,6$

$10:\; \; 6,4\; \; \; \; 5,5\; \; \; \; 4,6$

$9:\;\; \; 6,3\; \; \; \; 5,4\; \; \; \; 4,5\; \; \; \; 3,6$

This is a total of desired outcomes.

Probability is a fraction between and , where the numerator is the number of desired outcomes and the denominator is the total number of outcomes.

Therefore the probability is $\frac{10}{36}=\frac{5}{18}$ .

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ISEE Lower Level Math : Probability

Study concepts, example questions & explanations for ISEE Lower Level Math

All ISEE Lower Level Math Resources

Example Questions

Example Question #11 : How To Find The Probability Of An Outcome

Example Question #12 : How To Find The Probability Of An Outcome

Example Question #13 : How To Find The Probability Of An Outcome

Example Question #11 : How To Find The Probability Of An Outcome

Example Question #15 : How To Find The Probability Of An Outcome

Example Question #11 : Data Analysis And Probability

Example Question #17 : How To Find The Probability Of An Outcome

Example Question #18 : How To Find The Probability Of An Outcome

Example Question #11 : How To Find The Probability Of An Outcome

Example Question #11 : Probability

All ISEE Lower Level Math Resources

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