SAT Math : How to find the probability of an outcome

Study concepts, example questions & explanations for SAT Math

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Example Questions

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

In a bag, there are 6 black and 8 yellow marbles. A yellow marble is chosen at random and is not replaced. What is the probability of choosing a second yellow marble?

Possible Answers:

\dpi{100} \small \frac{6}{7}

\dpi{100} \small \frac{6}{13}

\dpi{100} \small \frac{7}{13}

\dpi{100} \small \frac{4}{7}

Correct answer:

\dpi{100} \small \frac{7}{13}

Explanation:

Because a yellow marble was selected and not replaced, there is a total of 13 marbles in the bag and of which, 7 are yellow; therefore, the probability of selecting a yellow marble is \dpi{100} \small \frac{7}{13}

Example Question #235 : Data Analysis

A couple has four children.  What is the probability of having exactly three girls?

Possible Answers:

Correct answer:

Explanation:

The total number of possibiliities is 16.  The outcome we are looking for is three girls and one boy which happens only four times.  Thus the probability becomes .

Example Question #71 : Outcomes

When a penny is flipped three times in a row, what is the probability of getting all heads or all tails?

Possible Answers:

Correct answer:

Explanation:

The sample space for three coin tosses in a row is 8.  Getting all heads can be done only one way.  Getting all tails can be done only one way.  So the probability of getting all heads or all tails is  or .

Example Question #237 : Data Analysis

A couple has three children.  What is the probability of having exactly two girls or two boys?

Possible Answers:

Correct answer:

Explanation:

The sample space for three children is 8.  We can count up what we want or subtract out what we don't want.  What we don't want is all boys or all girls.

So the probability becomes

Example Question #238 : Data Analysis

How many different ways can five books be lined up on a shelf?

Possible Answers:

Correct answer:

Explanation:

Order matters, so we use permutations.  _{5}^{5}\textrm{P} is

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

Jimmy is having trouble choosing what to wear to the baseball game.  He has six shirts, three pants, two pairs of socks and three pairs of shoes.  How many different outfits does Jimmy have to choose from?

Possible Answers:

Correct answer:

Explanation:

Choosing one of each clothing item is an independent event and should be multiplied together.  So the answer becomes 

or 

different combinations.

Example Question #240 : Data Analysis

Joe has eight marbles: 3 Red, 2 Green, 2 Blue and 1 Yellow.  

If Joe puts the marbles into a bag and draws out four, what are the odds that he gets exactly one of each color? 

Possible Answers:

\frac{1}{140}

\frac{3}{1024}

\frac{12}{140}

\frac{7}{1680}

\frac{1}{8}

Correct answer:

\frac{1}{140}

Explanation:

The probabilities of each pick changes as fewer marbles remain in the bag.  Each selection order of the colors will yield the same probability, expressed as:

Example Question #71 : Probability

If you flip a fair coin four times in a row, what is the probability of getting at least one head?

Possible Answers:

\frac{3}{8}

\frac{1}{16}

\frac{1}{4}

\frac{5}{8}

\frac{15}{16}

Correct answer:

\frac{15}{16}

Explanation:

1-P(no\ heads)=P(at\ least\ one\ heads)

There are 16 different ways to flip a fair coin four times in a row.  There is only one way to get all tails.

P(no\ heads)=\frac{1}{16}

so the P(at\ least\ one\ heads)=1-\frac{1}{16}=\frac{15}{16}

Example Question #72 : Probability

When rolling two standard six-sided dice, what is the probability of getting five or less?

Possible Answers:

\frac{3}{8}

\frac{5}{18}

\frac{5}{16}

\frac{1}{6}

\frac{7}{12}

Correct answer:

\frac{5}{18}

Explanation:

The sample space for rolling two six-sided dice is 36.

Counting the wanted outcomes gives:

2:  1,1 (1)

3: 1,2 and 2,1 (2)

4: 1,3 and 2,2 and 3,1 (3)

5: 1,4 and 2,3 and 3,2 and 4,1 (4)

So there are 10 ways to get a five or less.

Thus the probability of getting a five or less is \frac{10}{36}=\frac{5}{18}.

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

How many different ways can five books be lined up on a shelf?

Possible Answers:

120

75

225

90

25

Correct answer:

120

Explanation:

Order matters, so we use permutations:  _{5}^{5}\textrm{P}5\times 4\times 3\times 2\times 1=120.

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